which exponential functions have been simplified correctly check all that apply

Answer:

Option A, C, D, are the correct options.

Step-by-step explanation:

To check the exponential functions which have been simplified correctly we will take option one by one.

A). [tex]f(x)=5(\sqrt[3]{16})^{x}=5(\sqrt[3]{2^{4}})^{x}=5(2\sqrt[3]{2})^{x}[/tex]

B). [tex]f(x)=2.3(8^{\frac{1}{2}})^{x}=2.3(2.\sqrt{2})^{x}\neq 2.3(4^{x})[/tex]

C). [tex]f(x)=81^{\frac{x}{4}}=(3^{4})^{\frac{x}{4}}=(3^{\frac{4}{4}})^{x}=3^{x}[/tex]

D). [tex]f(x)=\frac{3}{4}(\sqrt{27})^{x}=\frac{3}{4}(\sqrt{3^{3}})^{x}=\frac{3}{4}.(3\sqrt{3})^{x}[/tex]

[tex]f(x)=(24)^{\frac{1}{3}x}=(2^{3}.3)^{\frac{1}{3}x}=(2.3^{\frac{1}{3}})^{x}\neq 2(\sqrt[3]{3})^{x}[/tex]

Exponential functions and their inverses like the natural logarithm are inverse functions, meaning they can undo each other. Simplifications like ln(e^x) result in x, and e^(ln x) simplifies to x. This property is integral to correctly simplifying exponential functions.

The exponential functions and their inverses, like the natural logarithm (ln), have specific properties where they can "undo" each other. This relationship allows us to simplify expressions involving exponentials and logarithms. For example, when you have ln(ex), this simplifies to x because the natural logarithm and the exponential function are inverse functions.

Similarly, when applying the exponential function to a natural logarithm, like eln(x), the result is just x. Furthermore, when taking square roots of exponentials, you can adjust the exponent to be evenly divisible by 2 and then take the square root of the base number, followed by dividing the exponent by 2. Also, while dividing exponentials, you subtract the exponents when the bases are the same.

Here is an example of this simplification: to compute the square root of e4, we can write it as e4/2, which simplifies to e2.

It is known that the depth of a lake at a point with coordinates (x, y) is z = 200 + 0.02x2 − 0.001y3, where x, y, and z are measured in meters. a woman in a kayak starts at the point (80, 60) and moves toward another point located at (0, 0). (a) find du f(80, 60). (give your answer correct to at least two decimal places.)

Nick can throw a baseball three more than 4 times the number of feet, f, that Jeff can throw the baseball. Which numbered expression can be used to find the number of feet that Nick can throw the ball?

In the figure, line m || line n. Find the measure of <7

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality 7.2b + 6.5 > 4.8b – 8.1. Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1. Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1. Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6. Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b. Which student’s first step was incorrect, and why? Amelia’s, because the variable term must be isolated on the left side Luis’s, because he flipped the inequality sign when he subtracted Shauna’s, because she did not apply the subtraction property of equality properly Clarence’s, because the terms he added together were not like terms

The reference angle for an angle whose measure is 260° is

On the first day of summer a rainstorm brought 2.29 inches of rain to the area. During the rest of the summer there was 3 times as much rain as on the first day. What was the total number of inches of rainfall for the summer?

A bag contains purple and orange marbles. Sam randomly takes out one marble and then returns it to the bag. He does this 18 times, and 12 of those times an orange marble is pulled out. What is P(green)?

The tooth fairy brings jack $5 plus $1 for each tooth that he loses. After jack loses a few teeth, the tooth fairy decides that he is paying too much money for teeth. He is gives jack $5 plus $0.50 for each tooth lost. Which graph shows the new function?

What's green and fluffy and comes from outer space?

Write 1.42 as a fraction or mixed number in simplest form.

what is the area of rhombus ABCD? do not round any steps

4.25 × 0.6 = 2.04 × 1.25

True
False

A salesperson receives a 3% commission on sales. The salesperson receives $180 in commission. What is the amount of sales?

Which expression is equivalent to 5(8 + 9)?

Which shows the image of ΔRST after the rotation (x, y) → (y, –x)?

The area of a rectangle is 45 square inches. The rectangle is 9 inches long. How wide is the rectangle?

A. 5 inches

B. 36 inches

C. 27 inches

D. 3 inches

Which operation flips the graph of a function over the x-axis?


A. Multiplying the function by –1
B. Multiplying the function by 1
C. Subtracting 1 from the function

For the standard normal probability distribution, the area to the right of the mean is:

Linear Programming HELP!! must answer both questions for brainliest and explain your answer.

At the market 8 batteries cost $10. How much will 6 batteries cost.

The volume of a cube with sides of length s is given by v = s3. find the rate of change of the volume with respect to s when s = 3 centimeters.

What is x and y. This is a geometry question

Select a counter-example that makes the conclusion false.

7 - 3 = 4, 8 - 5 = 3, 9 - 8 = 1

Conclusion: the difference of two positive numbers is always positive.

Counterexample:

how many solutions does
25-x=15-(3x+10)

a jewelry store is having a 10% off regular price sale. find the discount and the sale price of a ring normally priced at $1170

the discount is $[]
the sale price is $[]

Which angle is the included angle for MP¯¯¯¯¯¯ and MN¯¯¯¯¯¯¯ ?


∠M

∠N

∠P

Use geometry to evaluate (see attached) (calculus) the integral from 0 to 6 of the function f of x, dx for f of x equals 3 for x less than or equal to 3 and equals the quantity 6 minus x for x greater than 3.

27
13.5
12
10.5

ASAP PLEASE!!! Start with the following conditional statement: If it is October 31, then it is Halloween.
a. State the converse of the statement.
b. State the inverse of the statement.
c. State the contrapositive of the statement.

Given a right cone with base area b and height h, what is the formula for the volume?

Craig is training for a race. He bikes every 2 days and swims every 3 days. If he biked and swam today, how many days will pass before he bikes and swims on the same day again, the least common multiple of the numbers of days? Multiples of 2: 2, 4, 6, 8, 10, 12, . . . Multiples of 3: 3, 6, 9, 12, 15, 18, . . .

Answers:
1. 2 days
2. 3 days
3. 6 days
4. 12 days