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Which number equals [tex]$2^{-3}$[/tex]?
A. [tex][tex]$-6$[/tex][/tex] B. [tex]$-\frac{1}{8}$[/tex] C. [tex]$\frac{1}{8}$[/tex] D. [tex][tex]$\frac{1}{6}$[/tex][/tex]
To determine which number equals [tex]\( 2^{-3} \)[/tex]:
1. Understand the negative exponent: A negative exponent means taking the reciprocal of the base raised to the positive exponent. Therefore, [tex]\( 2^{-3} \)[/tex] can be rewritten as: [tex]\[
2^{-3} = \frac{1}{2^3}
\][/tex]
2. Calculate the positive exponent: Next, compute [tex]\( 2^3 \)[/tex]. This means multiplying 2 by itself three times: [tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
3. Find the reciprocal: Now, take the reciprocal of 8: [tex]\[
\frac{1}{2^3} = \frac{1}{8}
\][/tex]
So, [tex]\( 2^{-3} = \frac{1}{8} \)[/tex].
Therefore, the correct answer is: [tex]\[
\frac{1}{8}
\][/tex]
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