Question

Use the Power Rule of Exponents to simplify the expression (6^2)^4.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The Power Rule of Exponents states that when raising a power to another power, we multiply the exponents.

Using this rule, we can simplify the expression:

(6^2)^4 = 6^(2*4) = 6^8

Therefore, the simplified expression is 6^8.

Answer 2

Use the Power Rule of Exponents to simplify the expression (73^4)^5.(1 point)

Answer 3

[AI-generated answer — Bot GPT 3.5]

The Power Rule of Exponents states that when raising a power to another power, we multiply the exponents.

Using this rule, we can simplify the expression:

(73^4)^5 = 73^(4*5) = 73^20

Therefore, the simplified expression is 73^20.

Answer 4

Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12).(1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

The simplified expression using the Power Rule of Exponents is (12⋅12⋅12)⋅(12⋅12⋅12) = (12^3)⋅(12^3).

Using the Power Rule of Exponents, we can simplify further by multiplying the exponents:

(12^3)⋅(12^3) = 12^(3+3) = 12^6.

Therefore, the simplified equivalent expression is 12^6.

Answer 6

What exponent would make the two expressions equivalent: (16^x)^6=(16^18)?(1 point)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other:

(16^x)^6 = 16^18.

Now, we can use the power rule of exponents to multiply the exponents:

16^(x*6) = 16^18.

Since the bases 16 is the same and the exponents are equal, we can set the exponents equal to each other:

x*6 = 18.

Now, we can solve for x by dividing both sides of the equation by 6:

x = 18/6.

Simplifying the right side gives us:

x = 3.

Therefore, an exponent of 3 would make the two expressions equivalent.

Answer 8

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

Responses

A, 12^9
12 superscript 9 baseline

B. (−5)^0
left parenthesis negative 5 right parenthesis superscript 0 baseline

C, (7^8)⋅(7^10)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis

D, (7^4)^8

Answer 9

[AI-generated answer — Bot GPT 3.5]

The correct expression to use the Power Rule of Exponents is D, (7^4)^8.

This expression involves raising a power to another power, which allows us to apply the Power Rule of Exponents by multiplying the exponents together.

Answer 10

[AI-generated answer — Explain Bot]

To simplify the expression (6^2)^4 using the Power Rule of Exponents, you need to raise the base 6 to the power of the product of the exponents.

First, let's simplify the expression inside the parentheses. 6^2 means 6 raised to the power of 2, which is 6 * 6 = 36.

Now, we can rewrite the expression as 36^4.

To simplify further, you need to raise 36 to the power of 4, which means multiplying 36 by itself four times.

Calculating 36^4, we have:
36^4 = 36 * 36 * 36 * 36

Multiplying 36 by itself gives:
36 * 36 = 1296

Multiplying 1296 by 36 gives:
1296 * 36 = 46656

Multiplying 46656 by 36 gives:
46656 * 36 = 1679616

Therefore, the simplified expression is 1679616.