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Which is equal to $\frac{1}{2^7}$ ? $\newline$ Choices: $\newline$ (A) $2^{-7}$ $\newline$ (B) $-\frac{1}{(-2)^{-7}}$ $\newline$ (C) $\frac{1}{2^{-7}}$ $\newline$ (D) $(-2)^7$

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Understanding negative exponents

Full solution

Q. Which is equal to

\frac{1}{2^7}

?

\newline

Choices:

\newline

(A)

2^{-7}

\newline

(B)

-\frac{1}{(-2)^{-7}}

\newline

(C)

\frac{1}{2^{-7}}

\newline

(D)

(-2)^7

Understand expression $\frac{1}{2^7}$ : Step $1$ : Understand the expression $\frac{1}{2^7}$ . $\newline$ Rewrite $\frac{1}{2^7}$ using negative exponents. $\newline$ $\frac{1}{2^7} = 2^{-7}$
Rewrite using negative exponents: Step $2$ : Match the rewritten expression with the given choices. $\newline$ Compare $2^{-7}$ to each choice: $\newline$ (A) $2^{-7}$ matches exactly. $\newline$ (B) $-1/(-2)^{-7}$ does not match because of the negative signs and reciprocal. $\newline$ (C) $1/2^{-7}$ is the reciprocal of $2^7$ , not $2^{-7}$ . $\newline$ (D) $(-2)^7$ is not a reciprocal form and involves a negative base.

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