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 (7⋅7⋅7⋅7⋅7)10 left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline (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⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
The correct answer is: (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
To simplify the expression 715 using the Power Rule of Exponents, we have:
715 = 7^1 * 10^2 + 5 * 10^1 + 7^0 * 10^0
Using the expanded form of exponents, we can write this as:
715 = (7 * 7 * 7 * 7 * 7) * 10 * 10 + (7 * 7 * 7) * 10 + 1
Therefore, the expanded equivalent expression of 715 using the Power Rule of Exponents would be:
(7 * 7 * 7 * 7 * 7) * 10^2 + (7 * 7 * 7) * 10 + 1
To simplify the expression 715 using the Power Rule of Exponents, we need to decompose 715 into its prime factors and rearrange them using the exponentiation rules.
Prime factorization of 715: 715 = 5 * 11 * 13
Now, let's consider the options one by one:
Option 1: (7⋅7⋅7⋅7⋅7)10
This option represents 7 raised to the power of 10, which is not equivalent to the given expression.
Option 2: (718)3
This option represents 718 raised to the power of 3, which is not equivalent to the given expression.
Option 3: (710)5
This option represents 710 raised to the power of 5, which is not equivalent to the given expression.
Option 4: (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
This option correctly represents the expanded equivalent expression for 715.
So, the answer is option 4: (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7).