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9 Write
(16^(-3)*16^(-17))^(-23) in the form
16^(a).
(A)
256^(460)
(B)
256^(-460)
(C)
16^(460)
(D)
16^(-460)

$9$ Write $\left(16^{-3} \cdot 16^{-17}\right)^{-23}$ in the form $16^{a}$ . $\newline$ (A) $256^{460}$ $\newline$ (B) $256^{-460}$ $\newline$ (C) $16^{460}$ $\newline$ (D) $16^{-460}$

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Operations with rational exponents

Full solution

Q.

9

Write

\left(16^{-3} \cdot 16^{-17}\right)^{-23}

in the form

16^{a}

.

\newline

(A)

256^{460}

\newline

(B)

256^{-460}

\newline

(C)

16^{460}

\newline

(D)

16^{-460}

Combine Exponents: Rewrite the expression with combined exponents since they have the same base. $\newline$ (16^{-3} \times 16^{-17})^{-23} = 16^{-3 - 17}^{-23}
Add Exponents: Add the exponents inside the parentheses. $\newline$ $16^{(-3 - 17)} = 16^{-20}$
Power of a Power Rule: Now apply the power of a power rule by multiplying the exponents. $\newline$ $(16^{-20})^{-23} = 16^{-20 \times -23}$
Multiply Exponents: Multiply the exponents to simplify. $16^{(-20 \times -23)} = 16^{460}$
Check Answer Choices: Check the answer choices to find the correct one. $\newline$ The correct answer is $16^{460}$ , which matches option (C).

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