If the expression 715 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?
(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
(718)3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(7⋅7⋅7⋅7⋅7)10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline
(710)5
left parenthesis 7 superscript 10 baseline right parenthesis raised to the power of 5
left parenthesis 7 superscript 10 baseline right parenthesis to the power of 5
To simplify the expression 715 using the Power Rule of Exponents, we need to break down the number 715 into its prime factorization.
The prime factorization of 715 is 7 × 5 × 11.
Now, let's expand each option and see which one matches the simplified expression.
Option 1: (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
This option is multiplying the number 7 by itself 15 times.
Option 2: (718)3
This option is raising the number 7 to the power of 18 and then cubing it.
Option 3: (7⋅7⋅7⋅7⋅7)10
This option is multiplying the number 7 by itself 5 times and then raising the result to the power of 10.
Option 4: (710)5
This option is raising the number 7 to the power of 10 and then raising it to the power of 5.
From the given options, the expanded equivalent expression that matches the simplified expression 715 using the Power Rule of Exponents is Option 3:
(7⋅7⋅7⋅7⋅7)10, which means multiplying the number 7 by itself 5 times and then raising the result to the power of 10.