Which is equal to 1/84^2? Choices: (A)(-84)^2 (B)-84^2 (C)84^-2 (D)1/84^-2

Understand Expression: Understand the given expression 1/84^2. The given expression is a fraction where the numerator is 1 and the denominator is 84 raised to the power of 2. This is a positive exponent, so the base 84 is being squared in the denominator.Apply Negative Exponent Rule: Apply the negative exponent rule to find an equivalent expression. The negative exponent rule states that a^-m = 1/a^m. Therefore, if we want to express 1/84^2 with a negative exponent, we would write it as 84^-2.Compare with Choices: Compare the given choices with the equivalent expression 84^-2. (A) (-84)^2 is not equivalent because it represents a positive square of -84, not a fraction. (B) -84^2 is not equivalent because it represents the negative of 84 squared, not a fraction. (C) 84^-2 is equivalent because it represents 1/84^2 using the negative exponent rule. (D) 1/84^-2 is not equivalent because it would represent 1/(1/84^2), which simplifies to 84^2, not 1/84^2.

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Algebra 1

Negative exponents

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Q. Which is equal to

\frac{1}{84^2}

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Choices:

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(A)

(-84)^2

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(B)

-84^2

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(C)

84^{-2}

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(D)

\frac{1}{84^{-2}}

Understand Expression: Understand the given expression $\frac{1}{84^2}$ . The given expression is a fraction where the numerator is $1$ and the denominator is $84$ raised to the power of $2$ . This is a positive exponent, so the base $84$ is being squared in the denominator.
Apply Negative Exponent Rule: Apply the negative exponent rule to find an equivalent expression. $\newline$ The negative exponent rule states that $a^{-m} = \frac{1}{a^m}$ . Therefore, if we want to express $\frac{1}{84^2}$ with a negative exponent, we would write it as $84^{-2}$ .
Compare with Choices: Compare the given choices with the equivalent expression $84^{-2}$ .
(A) $(-84)^2$ is not equivalent because it represents a positive square of $-84$ , not a fraction.
(B) $-84^2$ is not equivalent because it represents the negative of $84$ squared, not a fraction.
(C) $84^{-2}$ is equivalent because it represents $1/84^2$ using the negative exponent rule.
(D) $1/84^{-2}$ is not equivalent because it would represent $1/(1/84^2)$ , which simplifies to $84^2$ , not $1/84^2$ .