Which is equal to 1/2^86? Choices: (A)-(-2)^86 (B)1/(-2)^-86 (C)-1/2^-86 (D)2^-86

Understand Expression: Understand the given expression 1/2^86. The expression 1/2^86 represents the reciprocal of 2 raised to the power of 86.Analyze Choices: Analyze the choices to find an equivalent expression. We need to find an expression that is equivalent to the given expression 1/2^86. (A) (-2)^86 is not equivalent because it represents a negative base raised to an even power, which would be positive and not a reciprocal.Check Choice (A): Check choice (B) 1/(-2)^-86. Using the negative exponent rule a^-m = 1/a^m, we can rewrite 1/(-2)^-86 as (-2)^86. This is not equivalent to 1/2^86 because the base is negative.Check Choice (B): Check choice (C) -1/2^-86. Using the negative exponent rule, we can rewrite -1/2^-86 as -2^86, which is not equivalent to 1/2^86 because of the negative sign.Check Choice (C): Check choice (D) 2^-86. Using the negative exponent rule, we can rewrite 2^-86 as 1/2^86, which is exactly the given expression.

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Which is equal to $\frac{1}{2^{86}}$ ? $\newline$ Choices: $\newline$ (A) $-(-2)^{86}$ $\newline$ (B) $\frac{1}{(-2)^{-86}}$ $\newline$ (C) $-\frac{1}{2^{-86}}$ $\newline$ (D) $2^{-86}$

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Q. Which is equal to

\frac{1}{2^{86}}

\newline

Choices:

\newline

(A)

-(-2)^{86}

\newline

(B)

\frac{1}{(-2)^{-86}}

\newline

(C)

-\frac{1}{2^{-86}}

\newline

(D)

2^{-86}

Understand Expression: Understand the given expression $\frac{1}{2^{86}}$ . The expression $\frac{1}{2^{86}}$ represents the reciprocal of $2$ raised to the power of $86$ .
Analyze Choices: Analyze the choices to find an equivalent expression. $\newline$ We need to find an expression that is equivalent to the given expression $\frac{1}{2^{86}}$ . $\newline$ (A) $(-2)^{86}$ is not equivalent because it represents a negative base raised to an even power, which would be positive and not a reciprocal.
Check Choice (A): Check choice (B) $1/(-2)^{-86}$ . Using the negative exponent rule $a^{-m} = 1/a^{m}$ , we can rewrite $1/(-2)^{-86}$ as $(-2)^{86}$ . This is not equivalent to $1/2^{86}$ because the base is negative.
Check Choice (B): Check choice (C) $-\frac{1}{2}^{-86}$ . $\newline$ Using the negative exponent rule, we can rewrite $-\frac{1}{2}^{-86}$ as $-2^{86}$ , which is not equivalent to $\frac{1}{2}^{86}$ because of the negative sign.
Check Choice (C): Check choice (D) $2^{-86}$ . Using the negative exponent rule, we can rewrite $2^{-86}$ as $1/2^{86}$ , which is exactly the given expression.