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]
