If the expression 715 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(718)3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(710)5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
(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)
The correct answer is:
(7⋅7⋅7⋅7⋅7)10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline
If the expression 715 is simplified using the Power Rule of Exponents, the expanded equivalent expression would be (7⋅7⋅7⋅7⋅7)10.
To simplify the expression 715 using the Power Rule of Exponents, we need to determine the prime factorization of the number 715.
The prime factorization of 715 is 5 * 11 * 13.
Now, let's look at the options:
- (718)3: This option does not involve the prime factors of 715.
- (710)5: This option also does not involve the prime factors of 715.
- (7⋅7⋅7⋅7⋅7)10: This option involves the prime factors of 715, but it is raising each factor to the power of 10, not 1, so it is not the expanded equivalent expression.
- (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7): This option involves the prime factors of 715 and raises each factor to the power of 1, which is the Power Rule of Exponents. Therefore, this is the expanded equivalent expression.
Therefore, the correct answer is (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7).