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
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)
To simplify (19^4)^9 using the Power Rule of Exponents, we can multiply the exponents:
(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?
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.
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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)
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.
To simplify the expression 7^15 using the Power Rule of Exponents, we need to apply the rule which states that when we raise a power to another power, we multiply the exponents.
In this case, we have 7 raised to the power of 15. Using the Power Rule of Exponents, we can expand it as follows:
(7^3)^5
Since 7^3 is equal to (7⋅7⋅7), we can substitute it back into the expression:
(7⋅7⋅7)^5
Now we can simplify further by multiplying:
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
So, the expanded equivalent expression would be:
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)