Question

Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses

(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline

(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline

(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis

129
Answer
Which of the following correctly used the Power Rule of Exponents in the expression (109)7?(1 point)
Responses

907
90 superscript 7 baseline

102
10 superscript 2 baseline

1063
10 superscript 63 baseline

1016
Answer
If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses

(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline

(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared

(45)2
left parenthesis 4 superscript 5 baseline right parenthesis squared

4⋅4⋅4⋅4⋅4⋅4⋅4
Answer
Use the Power Rule of Exponents to create an expression equivalent to (156)2.(1 point)
Responses

153
15 cubed

1512
15 superscript 12 baseline

154
15 superscript 4 baseline

158
Answer
What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses

8
8

15
15

21
21

27
27
Answer
can you find a solution?
Answer
can you please give me an option that i gave you?
Answered by GPT 3.5
None of the given options correctly use the Power Rule of Exponents. The Power Rule states that to raise a power to another power, you multiply the exponents. Therefore, the correct expression using the Power Rule would be:
(7^4)^8
Answered by GPT 3.5
The correct answer is

(10^9)^7 = 10^(9*7) = 10^63

Therefore, the corresponding option is:

1063
Answered by GPT 3.5
The correct answer is:

4⋅4⋅4⋅4⋅4⋅4⋅4
Answered by GPT 3.5
The correct answer is:

(15^6)^2 = 15^(6*2) = 15^12

Therefore, the corresponding option is:

1512
Answered by GPT 3.5
To find the exponent that would make the two expressions equivalent, we can set up an equation:

(3^3)^x = 324

Raising 3^3 to the power of x is the same as raising 3 to the power of 3x:

3^(3x) = 324

To solve for x, we can take the logarithm of both sides:

log(3^(3x)) = log(324)

Using the power rule of logarithms, we can bring down the exponent:

3x * log(3) = log(324)

Now we can solve for x by dividing both sides by log(3):

3x = log(324) / log(3)

Using a calculator, we can find:

3x ≈ 4.055

To solve for x, we can divide by 3:

x ≈ 4.055 / 3 ≈ 1.352

Therefore, the exponent that would make the two expressions equivalent is approximately 1.352.

None of the provided responses match the correct answer.
Answered by GPT 3.5
Apologies for the confusion earlier. Let's solve the equation (3^3)^x = 324.

(3^3)^x can be simplified to 27^x.

We are looking for an exponent x such that 27^x equals 324.

To find x, we can take the logarithm of both sides:

log(27^x) = log(324)

Using the logarithmic property, we can bring down the exponent:

x * log(27) = log(324)

Now we can solve for x by dividing both sides by log(27):

x = log(324) / log(27)

Using a calculator, we can find:

x ≈ 2

Therefore, the exponent that makes the two expressions equivalent is 2.
Answered by GPT 3.5
Apologies for the oversight. The option that matches the correct answer is:

8