Answer:
yes
Step-by-step explanation
because it is an algebraic expression. 3a + a are called like terms because they both contain the same letter. To simplify an expression we collect together like terms. You can only add or subtract when the letters are the same.
derivative of tanx? anyone?
Answer:
[tex]\displaystyle \frac{d}{dx}[\tan x] = \sec^2 x[/tex]
General Formulas and Concepts:
Pre-Calculus
Trigonometric IdentitiesCalculus
Differentiation
DerivativesDerivative NotationDerivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
*Note:
This is a known trigonometric derivative.
Step 1: Define
Identify
[tex]\displaystyle y = \tan x[/tex]
Step 2: Differentiate
Rewrite [Trigonometric Identities]: [tex]\displaystyle y = \frac{\sin x}{\cos x}[/tex]Derivative Rule [Quotient Rule]: [tex]\displaystyle y' = \frac{(\sin x)'\cos x - \sin x(\cos x)'}{\cos^2 x}[/tex]Trigonometric Differentiation: [tex]\displaystyle y' = \frac{\cos^2 x + \sin^2 x}{\cos^2 x}[/tex]Rewrite [Trigonometric Identities]: [tex]\displaystyle y' = \frac{1}{\cos^2 x}[/tex]Rewrite [Trigonometric Identities]: [tex]\displaystyle y' = \sec^2 x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The derivative of tanx in calculus is sec^2x, which represents the slope of the curve at any point x for the function tanx.
Explanation:The derivative of a function measures how the function changes as its input changes. In calculus, the derivative is a concept that describes the rate at which a quantity changes.
In the context of your question, the derivative of tanx or tangent x is sec^2x or secant squared x. This is a standard result that is usually memorized in calculus courses and can be derived using the limit definition of the derivative and trigonometric identities.
To put it in simpler terms, if tanx were the equation of a curve, the derivative (sec^2x) would represent the slope of that curve at any point x. This is key to understanding how the function behaves at different points and predicting its future behavior.
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an adult elephant that is 10ft tall casts a shadow that is 15ft long. find the length of the shadow that a 8ft telephone booth casts
Answer:
The length of the shadow the telephone booth is 12 ft.
Step-by-step explanation:
Given:
An adult elephant that is 10 ft tall casts a shadow that is 15 ft long.
The length of the telephone booth is 8 ft.
Now, to find the length of the shadow the telephone booth casts.
Let the length of the shadow the telephone booth be [tex]x.[/tex]
As given, an adult elephant that is 10 ft tall casts a shadow that is 15 ft long.
So, 10 ft is equivalent to 15 ft.
Thus, 8 ft is equivalent to [tex]x.[/tex]
Now, to get the length of the shadow of the booth we get cross multiplication method:
[tex]\frac{10}{15} =\frac{8}{x}[/tex]
By cross multiplying we get:
[tex]10x=120[/tex]
Dividing both sides by 10 we get:
[tex]x=12.[/tex]
Therefore, the length of the shadow the telephone booth is 12 ft.
-4+w+17-2/3w=16 solve the equation
Answer:
w=9
Step-by-step explanation:
I hope this image is helpful to you.
.
.
The student's algebra problem is solved by gathering like terms, simplifying the equation, and then isolating 'w'. The solution to the equation is 'w = 9'.
Explanation:The subject of this question is mathematics, specifically, the topic is algebra. The equation given is -4+w+17-2/3w=16. We need to solve this equation for 'w'.
To start, we should gather like terms. Therefore, -4 + 17 becomes 13, making our equation 13 + w - 2/3w = 16. We can also rearrange this to w - 2/3w instead, which results in 1/3w = 16 - 13, therefore, 1/3w = 3. To solve for w, we can multiply the both sides of the equation by 3, which leads to w = 3 * 3 or w = 9.
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xavier and yolanda have been married for exactly 40 years. yolanda is four years older than xavier now the sum of their ages is 126 how old was yolanda whwn they were married
Yolanda's was 25 years old when they were married.
Step-by-step explanation:
Let,
Age of Xavier = x
Age of Yolanda = x + 4
Combined age = 126
According to given statement;
Xavier's age + Yolanda's age = 126
[tex]x+(x+4)=126\\x+x+4=126\\2x=126-4\\2x=122\\[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{122}{2}\\x=61[/tex]
Yolanda's age = x+4 = 61+4 = 65
Age when married = 65 - 40 = 25
Yolanda's was 25 years old when they were married.
Keywords: word problems, addition
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Suppose Tommy walks from his home at (0, 0) to the mall at (0, 8), and then walks to a movie theater at (7, 8). After leaving the theater Tommy walks to the store at (7, 0) before returning home. If each grid square represents one block, how many blocks does he walk?
Answer:
If each grid square represents one block, then the number of box he walked will be 30 blocks.
Step-by-step explanation:
Tommy walks from his home to the mall and then walks to a movie theater.
His home is at (0,0), the mall is at (0,8) and the movie theater is at (7,8).
Now, distance from (0,0) to (0,8) is 8 units and the distance from (0,8) to (7,8) is 7 units.
So, total distance covered is (8 + 7) = 15 units.
After leaving the theater Tommy walks to the store before returning home.
The store is at (7,0).
Now, the distance from (7,8) to (7,0) is 8 units and the distance from (7,0) to (0,0) is 7 units.
So, total distance covered is (8 + 7) = 15 units.
If each grid square represents one block, then the number of the box he walked will be (15 + 15) = 30 blocks. (Answer)
Complete the set of ordered pairs for the relation.
{(x, y): y= 2(x + 11 and X E (-2,-1,0, 1, 2}}.
(2
Answer:
- 2
Step-by-step explanation:
I think this right!! Hope it helps!!
The complete set of ordered pairs for the relation y = 2(x + 11), where x belongs to the set (-2, -1, 0, 1, 2), is {(-2, 18), (-1, 20), (0, 22), (1, 24), (2, 26)}.
The given equation is y = 2(x + 11), where x takes values from the set (-2, -1, 0, 1, 2). To find the corresponding y-values for each x-value, we substitute the given x-values into the equation and calculate the y-values.
For x = -2:
y = 2(-2 + 11) = 2 * 9 = 18
So, the ordered pair is (-2, 18).
For x = -1:
y = 2(-1 + 11) = 2 * 10 = 20
Ordered pair: (-1, 20).
For x = 0:
y = 2(0 + 11) = 2 * 11 = 22
Ordered pair: (0, 22).
For x = 1:
y = 2(1 + 11) = 2 * 12 = 24
Ordered pair: (1, 24).
For x = 2:
y = 2(2 + 11) = 2 * 13 = 26
Ordered pair: (2, 26).
Combining all these ordered pairs, we have the complete set of ordered pairs for the given relation:
{(-2, 18), (-1, 20), (0, 22), (1, 24), (2, 26)}.
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Zack watered his garden with 1 3/8
gallons of water the first week he planted it. He
watered it with 1 3/4 gallons the second week, and
2 1/8 gallons the third week. If he continued watering
in this pattern, how much water did he use on the
fifth week?
A 22 gallons
© 34 gallons
B 27 gallons
0 6 gallons
Answer:
The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.
Step-by-step explanation:
Let's find out the pattern Zack is using to water his garden, this way:
First week = 1 3/8 gallons of water
Second week = 1 3/4 gallons of water = 1 3/8 + 3/8 = 1 6/8 = 1 3/4
Third week = 2 1/8 gallons of water = 1 3/4 + 3/8 = 1 6/8 + 3/8 = 2 1/8
The constant of adding every week is 3/8 gallons, therefore,
Fourth week = 2 1/8 + 3/8 = 2 4/8 = 2 1/2 gallons of water
Fifth week = 2 1/2 + 3/8 = 2 4/8 + 3/8 = 2 7/8 gallons of water
The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.
Following the pattern of increasing water usage by 3/8 gallons each week, Zack will use 2 7/8 gallons of water in the fifth week.
Zack watered his garden with increasing amounts of water over the first three weeks. Since there is a pattern, we can deduce the amount of water he will use in the fifth week by identifying the pattern and then continuing it.
Week 1: 1 3/8 gallonsWeek 2: 1 3/4 gallonsWeek 3: 2 1/8 gallonsObserving the pattern, we see that Zack is increasing the amount of water by 3/8 gallons each week. The progression in gallons is:
Week 1: 1 3/8Week 2: 1 3/8 + 3/8 = 1 3/4Week 3: 1 3/4 + 3/8 = 2 1/8Continuing this pattern:
Week 4: 2 1/8 + 3/8 = 2 1/2Week 5: 2 1/2 + 3/8 = 2 7/8Therefore, Zack will use 2 7/8 gallons of water on the fifth week.
What’s the correct way to read 43.106
To read 43.106 correctly, say 'forty-three point one zero six'
Explanation:To read the number 43.106 correctly, we start by reading the whole number part, which is 43. This is read as 'forty-three'.
Next, we read the decimal part. The first digit after the decimal point is read as 'one', the second digit as 'zero', and the third digit as 'six'. Finally, we put all the parts together and read the number as 'forty-three point one zero six'.
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Which law would you use to simplify the expression
(p\q)3
Answer:3√(p/q)3
Step-by-step explanation: Find the cube root .
The law used to simplify the expression [tex]( (p/q)^3 \)[/tex] is the "Power of a Quotient" rule.
The correct option is (b).
The "Power of a Quotient" rule states that when a fraction is raised to a power, we can raise both the numerator and denominator to that power individually. Mathematically, it is represented as:
[tex]\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \][/tex]
Applied to the expression [tex]\( (p/q)^3 \)[/tex], we raise both[tex]\( p \) and \( q \)[/tex] to the power of 3:
[tex]\[ \left(\frac{p}{q}\right)^3 = \frac{p^3}{q^3} \][/tex]
This simplification allows us to express the original expression in terms of powers of the numerator and denominator separately. In other words, the exponent 3 is distributed to both [tex]\( p \) and \( q \), resulting in \( p^3 \)[/tex]in the numerator and [tex]\( q^3 \)[/tex] in the denominator.
Using this rule, we can handle expressions involving powers of fractions efficiently, breaking them down into simpler terms that are easier to work with or evaluate. It's particularly useful when dealing with algebraic expressions or equations where fractions with powers are involved, providing a systematic approach to simplification.
complete question given below:
Which law would you use to simplify the expression
[tex](p\q)^3[/tex]?
a.power of a power
b.power of a quotient
c.quotient of powers
d.power of a product
) On a number line, what is the distance between -5 and -3? Respond in terms of absolute value.
Answer:
2
Step-by-step explanation:
There are 2 units of distance separating -5 and -3.
What solves 4 + 1/5x = -1 ?
Answer: [tex]x=-25[/tex]
Step-by-step explanation:
For this exercise it is necessary to remember the multiplication of signs:
[tex](+)(+)+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-[/tex]
Then, having the following equation provided in the exercise:
[tex]4 + \frac{1}{5}x = -1[/tex]
You need to solve for the variable "x" in order to find its value.
To solve the equation, you can follow the steps shown below:
Step 1: You need to subtract 4 from both sides of the equation. Then:
[tex]4 + \frac{1}{5}x-(4) = -1-(4)\\\\ \frac{1}{5}x=-1-4\\\\ \frac{1}{5}x=-5[/tex]
Step 2: This is the final step. You must multiply both sides of the equation by 5 in order to find the value of the variable "x".
Then, you get the following result:
[tex](5)( \frac{1}{5}x)=(-5)(5)\\\\x=-25[/tex]
Can somebody please help me with these two questions? And show your work please?
Solve for x.
(1) x = 12, (2) [tex]x=3\frac{1 }{2}[/tex]
Solution:
(1) If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.
⇒ [tex]\frac{25}{10}=\frac{30}{x}[/tex]
Do cross multiply.
⇒ [tex]25 \times x=30 \times 10[/tex]
Divide both sides of the equation by 25 to equal the expression.
⇒ [tex]x=\frac{30 \times 10}{25}[/tex]
⇒ x = 12
(2) Side of triangle = [tex]4\frac{1}{3} =\frac{13}{3}[/tex]
If the two triangles are similar and the angles of two triangles are congruent then the corresponding sides are in proportion.
⇒ [tex]\frac{26}{\frac{13}{3} }=\frac{21}{x}[/tex]
Do cross multiply.
⇒ [tex]26 \times x=21 \times \frac{13}{3}[/tex]
⇒ [tex]26 \times x=7 \times 13[/tex]
Divide both sides of the equation by 26 to equal the expression.
⇒ [tex]x=\frac{7 \times 13}{26}[/tex]
⇒ [tex]x=\frac{7 }{2}[/tex]
⇒ [tex]x=3\frac{1 }{2}[/tex]
h(x)=0.00004668x^3 find h(x/1.6)
Answer:
0.00019120128
Step-by-step explanation:
1.6x1.6x1.6 x .00004668
The length of a rectangle is 6 inches more than it’s width. if the perimeter of the rectangle is 24 inches, find the dimensions. create let statement and write equation.
Answer:
The dimensions of the rectangle are;
Width = 3 inches
Length = 9 inches
Step-by-step explanation:
Given;
Perimeter of the rectangle is 24 inches Length is 6 inches more than the widthWe want to determine the dimensions of the rectangle;
Let the width of the rectangle be x inchesThis means, the length of the rectangle will be (x+6) inchesBut, Perimeter = 2(L+W)Forming an equation, we get;
2 ( x + x + 6) = 24
4x + 12 = 24
With the equation we can solve for x
4x = 24 - 12
4x = 12
x = 3
and (x + 6) = 9
Therefore;
Width = 3 inches
Length = 9 inches
The width of the rectangle is 3 inches and the length is 9 inches.
Let's assume that the width of the Rectangle dimensions is represented by 'w' inches.
Since the length is 6 inches more than the width, we can represent it as 'w + 6' inches.
The perimeter of a rectangle is the sum of all its sides.
In this case, the formula for the perimeter is 2(w + l), where w represents the width and l represents the length.
So, for this problem, we have the equation 2(w + w + 6) = 24.
Simplifying this equation, we get 4w + 12 = 24.
Solving for 'w', we find that the width is 3 inches.
Plugging this value back into the equation for the length, we find that the length is 9 inches.
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Ruby has a collection of 16 stuffed animals. She gives 1/4 of her collection to her younger brother. Then she gives half of the remaining animals to her baby sister. How many animals does Ruby give her sister
Answer:
6
Step-by-step explanation:
16/4=4 (to brother) 16-4=12 (whats remaining) 12/2=6 (to sister)
Ruby gives her sister 6 animals.
Explanation:To find out how many animals Ruby gives her sister, we need to follow the instructions step by step. Ruby starts with 16 stuffed animals. She gives 1/4 of her collection to her brother, which is equal to 16 * 1/4 = 4. Now Ruby has 16 - 4 = 12 stuffed animals left. Then she gives half of the remaining animals to her sister, which is equal to 12 * 1/2 = 6. So Ruby gives her sister 6 animals.
19=15w-4(3w-1)
What is the answer to this problem
Answer:
w=5
Step-by-step explanation:
First you have to write out the equation. Then you distribute negative 4 to 3w then you distribute -4 to -1 you get 4. Then you need to combine like terms and you get 3W. then you need to subtract four from each side you get 15 equals 3W then divide aside by three and you get W equals five
Darius uses 6 2/3 cup of bread cubes to make a batch of stuffing for his family. How many cups of bread cubes will he need to make four batches of stuffing for a family reunion? *
Answer:
Darius needs [tex]26\frac{2}{3}[/tex] cups of bread cubes to make four batches of stuffing for a family reunion.
Step-by-step explanation:
Given:
bread cubes to make a batch of stuffing = 6 2/3 cup
To Find:
Number of cups of bread cubes needed to make four batches of stuffing for a family reunion = ?
Solution:
According to the question, to make one batch of stuffing Darius needs [tex]6\frac{2}{3}[/tex] cups of bread cubes
So if he wants to make four batched, then the number of cups of bread cubes will be four times as needed for making one batch
Then
Number of cups of bread cubes needed to make four batches = 4 x bread cubes needed to make a batch of stuffing
Number of cups of bread cubes needed to make four batches
= [tex]4 \times 6\frac{2}{3}[/tex]
=>[tex]4 \times \frac{18+2}{3}[/tex]
=> [tex]4 \times \frac{20}{3}[/tex]
=>[tex]\frac{80}{3}[/tex]
=>[tex]26\frac{2}{3}[/tex]
Darius will need 80/3 cups of bread cubes to make four batches of stuffing for a family reunion.
Explanation:To find out how many cups of bread cubes Darius will need to make four batches of stuffing for a family reunion, we need to multiply the amount of bread cubes used in one batch by the number of batches he wants to make. Darius uses 6 2/3 cups of bread cubes in one batch. So, to find the total amount of bread cubes needed for four batches, we can multiply 6 2/3 cups by 4.
First, we convert the mixed number into an improper fraction: 6 2/3 = (6 * 3 + 2)/3 = 20/3.
Next, multiply the improper fraction by 4: (20/3) * 4 = 80/3 cups.
Therefore, Darius will need 80/3 cups of bread cubes to make four batches of stuffing for a family reunion.
Simplify: (5x^6y^-4)^3(2x^8y^3)
Answer:
see attached picture please
A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month.
The relationship between the number of months after the first year and the amount remaining on the card is .
The independent variable is the _____________?
The dependent variable is the ______________?
Answer:
The relationship between the number of months after the first year and the amount on the remaining card is linear and inverse (which means that, when the number of montsh after the first year increases, the amount on the remaining car decreases, in a linear way).The independent variable is the numbers of months after the first year.The dependent variable is the amount on the remaining card, because this amount depends on the time it has passed since the first year (which is our independent variable!).If we call "y" our dependent variable, and "x" our independent variable, this relationship can be written as y=25 - 2.5x. If no months has passed since the first year, then x=0 and the amount in the card equals $25, while if one month has passed since the first year x=1 and y=22.5 (the amount in the card in this case is $22.5).Answer:
The relationship between the number of months after the first year and the amount remaining on the card is discrete
The independent variable is the
number of months after the first year
The dependent variable is the
amount remaining on the card.
The line plot represents how many trips 10 adults take to the gas station in a month. After 4 more adults are included in the data the mode decreases and the median increases. Which could be the new graph
Answer:
Step-by-step explanation:it is the second option. :)
Answer:
Top right = second choose
Step-by-step explanation:
simplify: 3x-9+13x-6 show solution
Answer:16x-15
Step-by-step explanation:
3x-9+13x-6
Collect like terms
3x+13x-9-6
16x-15
^^ Does anyone know the answer?
Answer:
60 degrees
Step-by-step explanation:
180-90=90
90-30=60
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
Quadrilateral ABCD has diagonals that are congruent and perpendicular to each other. What classification can be given to ABCD? (5 points) Parallelogram Rectangle Rhombus Square
Answer:
Square
Got it correct on my test just now
A quadrilateral had vertices (2,0) (0,-2) (-2,4) and (-4,2) which special quaderalateral is formed by connecting the midpoints of the sides
Answer:
The special quadrilateral formed by connecting the midpoints of the sides of the original quadrilateral is : a rhombus
Step-by-step explanation:
Look at the photo below for the figure
:)
the height of a parallelogram is 18 centimeters less than its base. if the area is 175 square centimeters, what is its height?
The height of a parallelogram can be found by solving the equation 'Area = base × height' given the area is 175 square centimeters and the height is 18 centimeters less than the base. The base 'b' and the height 'b - 18' form a quadratic equation that can be solved to find 'b', after which subtracting 18 will give the height.
Explanation:The question is asking to find the height of a parallelogram given its area and a relationship between the base and the height. The area of a parallelogram is found using the formula Area = base × height. According to the given information, we know that the area is 175 square centimeters. The relationship between the base and the height of the parallelogram is such that the height is 18 centimeters less than the base. Therefore, we can denote the base as 'b' and the height as 'b - 18'. Plugging these into the formula for the area we get 175 = b × (b - 18).
To solve for 'b', we can set up and solve a quadratic equation. After finding the value of 'b', we can calculate the height by subtracting 18 centimeters from our value for 'b'. Let's go through the steps:
175 = b × (b - 18).Distribute the 'b' on the right side of the equation: 175 = b^2 - 18b.Rearrange to form a quadratic equation: b^2 - 18b - 175 = 0.Solve the quadratic equation using the quadratic formula or factorization (if possible).Substitute the positive value of 'b' back into 'b - 18' to find the height.After solving the quadratic equation, we would get the value of 'b' and accordingly the value of 'b - 18' which is the height of the parallelogram in centimeters.
trent has a collection of 198 baseball and basketball training cards. he has 4.5 times as many baseball cards as basketball cards. how many baseball cards does trent have in his collection?
There are 162 base ball cards
Solution:
Let "a" be the number of baseball training cards
Let "b" be the number of basket ball training cards
Trent has a collection of 198 baseball and basketball training cards
Therefore,
a + b = 198 -------- eqn 1
He has 4.5 times as many baseball cards as basketball cards
Number of baseball cards = 4.5(number of basketball cards)
a = 4.5b --------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 2 in eqn 1
4.5b + b = 198
5.5b = 198
b = 36
Substitute b = 36 in eqn 2
a = 4.5(36)
a = 162
Thus there are 162 base ball cards
Trent have 162 baseball cards in his collection.
Trent has a collection of 198 baseball and basketball training cards, with baseball cards being 4.5 times as many as basketball cards. To find out how many baseball cards Trent has, we can set up a system of equations.
Let x be the number of basketball cards.
Since the number of baseball cards is 4.5 times the number of basketball cards, the number of baseball cards is 4.5x.
The total number of cards is 198, so x + 4.5x = 198.
Solving this equation, we find x = 36. Therefore, the number of baseball cards Trent has is 4.5*36 = 162 baseball cards.
Which fraction is bigger
1 1/6 or 1 4/12
Answer:
1 1/6
Step-by-step explanation:
because it takes more to get to 12 than 6
11/6 is bigger because if you convert both into decimal form
11/6=1.83
14/12=1.16
A bottle of sugar syrup soda had 3 3/9 grams of sugar in it. If Will drank 2 full bottles and 1/2 of a bottle, how many grams of sugar did her drink?
Will drank [tex]8\frac{1}{3}[/tex] grams of sugar.
Step-by-step explanation:
Given,
Amount of sugar in one bottle = [tex]3\frac{3}{9}=\frac{30}{9}\ grams[/tex]
Amount of bottles drank by Will = [tex]2+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}\ bottles[/tex]
Total sugar drank by Will = Amount of sugar in one bottle * Amount of bottles drank by Will
Total sugar drank by Will = [tex]\frac{30}{9}*\frac{5}{2}[/tex]
Total sugar drank by Will = [tex]\frac{150}{18}=\frac{25}{3}[/tex]
Total sugar drank by Will = [tex]8\frac{1}{3}[/tex]
Will drank [tex]8\frac{1}{3}[/tex] grams of sugar.
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The square of the quantity 17 less than x
What is Cube root of 125 x Superscript 12?
A. 5x2
B. 5x4
C. 25x2
D. 25x4
==============================================
Work Shown:
125 = 5*5*5 = (5)^3
x^12 = (x^4)*(x^4)*(x^4) = (x^4)^3
125x^12 = (5x^4)^3
[tex]\large \sqrt[3]{125x^{12}} = \left(125x^{12}\right)^{1/3}[/tex]
[tex]\large \sqrt[3]{125x^{12}} = \left((5x^4)^3\right)^{1/3}[/tex]
[tex]\large \sqrt[3]{125x^{12}} = (5x^4)^{3*(1/3)}[/tex]
[tex]\large \sqrt[3]{125x^{12}} = (5x^4)^{1}[/tex]
[tex]\large \sqrt[3]{125x^{12}} = \textbf{5x}^{\textbf{4}}[/tex]
Answer:
Step-by-step explanation:
[tex]125=5*5*5=5^{3}\\\\\ \sqrt[3]{125x^{12}}=\sqrt[3]{125*x^{4*3}}\\\\=\sqrt[3]{5^{3}*(x^{4})^{3}}=5*x^{4}=5x^{4}[/tex]