Question
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⋅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
Responses
(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
Answers
GPT 3.5
left parenthesis 7 superscript 10 baseline right parenthesis to the power of 5
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .(1 point)
GPT 3.5
To simplify (19^4)^9 using the Power Rule of Exponents, we can multiply the exponents:
(19^4)^9 = 19^(4*9) = 19^36
(19^4)^9 = 19^(4*9) = 19^36
Apply the Property of Negative Integer Exponents to solve 7^−3 . The answer should not contain any exponent expression or decimals.(1 point)
Is it 0.007?
Is it 0.007?
GPT 3.5
No, the answer is not 0.007.
To solve 7^(-3) using the Property of Negative Integer Exponents, we can rewrite it as the reciprocal of 7^3:
7^(-3) = 1 / 7^3 = 1 / (7 * 7 * 7) = 1 / 343
So, the answer is 1/343.
To solve 7^(-3) using the Property of Negative Integer Exponents, we can rewrite it as the reciprocal of 7^3:
7^(-3) = 1 / 7^3 = 1 / (7 * 7 * 7) = 1 / 343
So, the answer is 1/343.
oh
GPT 3.5
No problem! Please let me know if there's anything else I can help you with.
Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7 . Show your work and explain how you used the product rule of integer exponents.(2 points)
GPT 3.5
To apply the product rule of integer exponents to find the numerical equivalent of 12^(-5) * 12^7, we can use the rule which states that when multiplying two terms with the same base, we can add their exponents.
First, let's rewrite the expression using the product rule:
12^(-5) * 12^7 = 12^((-5) + 7)
Now, we simplify the exponent:
12^((-5) + 7) = 12^2
Finally, we can find the numerical equivalent by evaluating 12^2:
12^2 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.
First, let's rewrite the expression using the product rule:
12^(-5) * 12^7 = 12^((-5) + 7)
Now, we simplify the exponent:
12^((-5) + 7) = 12^2
Finally, we can find the numerical equivalent by evaluating 12^2:
12^2 = 144
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144.