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

9 answers

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.
Use the Power Rule of Exponents to simplify the expression (73^4)^5.(1 point)
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.
Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12).(1 point)
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.
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)?(1 point)
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.
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
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.