Use the Power Rule of Exponents to simplify (10^3)^6 .(1 point)

Answer 1

To simplify (10^3)^6 using the power rule of exponents, we multiply the exponents.

10^(3*6) = 10^18.

Therefore, the simplified form of (10^3)^6 is 10^18.

Answer 2

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)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 superscript 5 baseline

(718)3
left parenthesis 7 superscript 18 baseline right parenthesis cubed

(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

Answer 3

The expanded equivalent expression for 7^15 using the Power Rule of Exponents would be:

(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)

So the correct response is:

(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)

Answer 4

Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .

Answer 5

To simplify (19^4)^9 using the Power Rule of Exponents, we multiply the exponents.

(19^4)^9 = 19^(4*9)

= 19^36

Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.

Answer 6

Apply the Property of Negative Integer Exponents to solve 7^−3 . The answer should not contain any exponent expression or decimals.(1 point)

Answer 7

Using the Property of Negative Integer Exponents, we know that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent.

Therefore, 7^(-3) can be rewritten as 1/(7^3).

Simplifying further, 7^3 is equal to 7 * 7 * 7, which is equal to 343.

So, 7^(-3) is equal to 1/343.

Therefore, the solution to 7^(-3) is 1/343.

Answer 8

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only.(1 point)

Answer 9

Using the Property of Negative Integer Exponents, we can rewrite 3^(-17) as the reciprocal of 3^(17) and 8^(-14) as the reciprocal of 8^(14).

Therefore, 3^(-17)/8^(-14) can be rewritten as (1/3^(17))/(1/8^(14)).

Simplifying further, we can multiply by the reciprocal of the denominator, which would be 8^(14)/1.

So, (1/3^(17))/(1/8^(14)) is equivalent to (1/3^(17))*(8^(14)/1).

Now, in order to have positive exponents only, we can flip the reciprocals and change the signs of the exponents.

Therefore, (1/3^(17))*(8^(14)/1) is equivalent to (8^(14))/(3^(17)).

Therefore, an expression equivalent to 3^(-17)/8^(-14) with positive exponents only is (8^(14))/(3^(17)).