Which is equal to 3^-49? Choices: (A)(-3)^-49 (B)1/3^49 (C)-(-3)^49 (D)1/(-3)^-49

Understand expression: Understand the expression 3^-49. Identify the base and the exponent. In 3^-49, 3 is the base raised to the exponent -49. Base: 3 Exponent: -49Apply negative exponent rule: Apply the negative exponent rule to 3^-49. Negative exponent rule: a^-m = 1 / a^m So, 3^-49 = 1 / 3^49Match with given choices: Match the expression 1 / 3^49 with the given choices. (A) (-3)^-49 is not correct because the base is -3, not 3. (B) 1/3^49 is the correct expression, as it matches the result from Step 2. (C) -(-3)^49 is not correct because it represents a negative value, not a reciprocal. (D) 1/(-3)^-49 is not correct because the base is -3 and the exponent is -49, which would result in a double negative exponent, not matching our result.

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Algebra 1

Negative exponents

Full solution

Q. Which is equal to

3^{-49}

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Choices:

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(A)

(-3)^{-49}

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(B)

\frac{1}{3^{49}}

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(C)

-(-3)^{49}

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(D)

\frac{1}{(-3)^{-49}}

Understand expression: Understand the expression $3^{-49}$ . Identify the base and the exponent. In $3^{-49}$ , $3$ is the base raised to the exponent $-49$ . Base: $3$ Exponent: $-49$
Apply negative exponent rule: Apply the negative exponent rule to $3^{-49}$ . $\newline$ Negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^{m}}$ $\newline$ So, $3^{-49} = \frac{1}{3^{49}}$
Match with given choices: Match the expression $\frac{1}{3^{49}}$ with the given choices. $\newline$ (A) $(-3)^{-49}$ is not correct because the base is $-3$ , not $3$ . $\newline$ (B) $\frac{1}{3^{49}}$ is the correct expression, as it matches the result from Step $2$ . $\newline$ (C) $-(-3)^{49}$ is not correct because it represents a negative value, not a reciprocal. $\newline$ (D) $\frac{1}{(-3)^{-49}}$ is not correct because the base is $-3$ and the exponent is $-49$ , which would result in a double negative exponent, not matching our result.