Answer :
To find an expression equivalent to [tex]\( (-2)^{-3} \)[/tex], let's break it down step by step:
1. Understand the Negative Exponent: A negative exponent means you take the reciprocal of the base raised to the positive of that exponent. So, [tex]\( x^{-n} = \frac{1}{x^n} \)[/tex].
2. Apply the Rule: For the expression [tex]\( (-2)^{-3} \)[/tex], applying the above rule means:
[tex]\[
(-2)^{-3} = \frac{1}{(-2)^3}
\][/tex]
3. Calculate [tex]\( (-2)^3 \)[/tex]:
- First, find [tex]\((-2)^3\)[/tex]. This means multiplying [tex]\(-2\)[/tex] by itself three times:
[tex]\[
(-2) \times (-2) \times (-2) = 4 \times (-2) = -8
\][/tex]
4. Determine the Reciprocal:
[tex]\[
\frac{1}{(-2)^3} = \frac{1}{-8}
\][/tex]
This result is equivalent to [tex]\(-\frac{1}{8}\)[/tex].
Hence, the expression [tex]\( (-2)^{-3} \)[/tex] is equivalent to [tex]\(-\frac{1}{8}\)[/tex], which corresponds to choice A.
1. Understand the Negative Exponent: A negative exponent means you take the reciprocal of the base raised to the positive of that exponent. So, [tex]\( x^{-n} = \frac{1}{x^n} \)[/tex].
2. Apply the Rule: For the expression [tex]\( (-2)^{-3} \)[/tex], applying the above rule means:
[tex]\[
(-2)^{-3} = \frac{1}{(-2)^3}
\][/tex]
3. Calculate [tex]\( (-2)^3 \)[/tex]:
- First, find [tex]\((-2)^3\)[/tex]. This means multiplying [tex]\(-2\)[/tex] by itself three times:
[tex]\[
(-2) \times (-2) \times (-2) = 4 \times (-2) = -8
\][/tex]
4. Determine the Reciprocal:
[tex]\[
\frac{1}{(-2)^3} = \frac{1}{-8}
\][/tex]
This result is equivalent to [tex]\(-\frac{1}{8}\)[/tex].
Hence, the expression [tex]\( (-2)^{-3} \)[/tex] is equivalent to [tex]\(-\frac{1}{8}\)[/tex], which corresponds to choice A.