If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(7⋅7⋅7⋅7⋅7)^10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis
(7^18)^3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(7^10)^5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
To simplify the expression 7^15 using the Power Rule of Exponents, we need to multiply the exponents.
The correct expanded equivalent expression would be:
(7^15) = (7^10) * (7^5)
Therefore, the correct answer is (7^10)^5.
To simplify the expression 7^15 using the Power Rule of Exponents, we need to multiply the exponents when raising a power to a power.
The Power Rule states that (a^m)^n is equal to a^(m*n).
So, let's apply the Power Rule to the given expression:
7^(15)
= (7^1)^15 (7 to the power of 1 is just 7, so we can rewrite it as 7^1)
= 7^(1*15) (Applying the Power Rule)
= 7^15 (Simplifying the exponent)
Therefore, the simplified expression of 7^15 is 7^15 itself.
Out of the given options, none of them represent an expanded equivalent expression of 7^15 because there is no need to expand it further.