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Select all the expressions that are equivalent to $(5^{-5})^3$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{5^{15}}$ $\newline$ (B) $\frac{1}{5^{-2}}$ $\newline$ (C) $5^{-15}$ $\newline$ (D) $5^{-2}$

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Simplify exponential expressions using exponent rules

Full solution

Q. Select all the expressions that are equivalent to

(5^{-5})^3

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{5^{15}}

\newline

(B)

\frac{1}{5^{-2}}

\newline

(C)

5^{-15}

\newline

(D)

5^{-2}

Simplify expression: Step $1$ : Simplify the expression $(5^{-5})^3$ . Using the power of a power rule, $(a^m)^n = a^{m*n}$ , $(5^{-5})^3 = 5^{-5*3} = 5^{-15}$
Compare with choices: Step $2$ : Compare the simplified expression with the choices. $\newline$ $5^{-15}$ is the same as $1/5^{15}$ , so (A) is correct. $\newline$ $5^{-15}$ is not the same as $1/5^{-2}$ or $5^{-2}$ , so (B) and (D) are incorrect. $\newline$ $5^{-15}$ matches exactly with (C), so (C) is also correct

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