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

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Understanding negative exponents

Full solution

Q. Which is equal to

7^{-2}

?

\newline

Choices:

\newline

(A)

-(-7)^2

\newline

(B)

\frac{1}{7^2}

\newline

(C)

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

\newline

(D)

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

Identify expression meaning: Identify the expression $7^{-2}$ and understand its meaning. $\newline$ $7^{-2}$ means $1$ divided by $7$ squared ( $7^2$ ). $\newline$ Calculation: $7^{-2} = 1 / 7^2$
Calculate $7^{-2}$ : Compare the given choices to find an equivalent expression. $\newline$ (A) $-(-7)^2 = -49$ (This is not equivalent to $1/49$ .) $\newline$ (B) $1/7^2 = 1 / 49$ (This matches our calculation.) $\newline$ (C) $-1/(-7)^{-2} = -1 / (1/49) = -49$ (This is not equivalent to $1/49$ .) $\newline$ (D) $-1/7^{-2} = -1 / (1/49) = -49$ (This is not equivalent to $1/49$ .)

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