Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
(-2)^{-3} = -\frac{1}{8}
\]
Solution
To evaluate \( (-2)^{-3} \), follow these steps:
1. **Understand Negative Exponents**:
A negative exponent indicates the reciprocal of the base raised to the positive exponent.
\[
(-2)^{-3} = \frac{1}{(-2)^3}
\]
2. **Calculate the Positive Exponent**:
Compute \( (-2)^3 \):
\[
(-2)^3 = (-2) \times (-2) \times (-2) = -8
\]
3. **Find the Reciprocal**:
Substitute back into the equation:
\[
\frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8}
\]
**Final Answer**:
\[
(-2)^{-3} = -\frac{1}{8}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
To evaluate \( (-2)^{-3} \), remember that a negative exponent indicates a reciprocal. So, \( (-2)^{-3} \) can be rewritten as \( \frac{1}{(-2)^3} \). Calculating \( (-2)^3 \), we find that it equals \(-8\), giving us \( \frac{1}{-8} \), or simply \(-\frac{1}{8}\). Voila, your final answer is \( -\frac{1}{8} \)! Now, if you want to dazzle your friends, here’s a cool trick: always remember that negative numbers raised to an odd power remain negative, while those raised to an even power become positive. It’s like a little dance for numbers! So next time you encounter a negative base, just identify the exponent’s flavor, and you’ll get the answer right every time!
