Question
Simplity the follo \[ \left(x^{8} y^{5}\right)^{-5} \]
Ask by Phillips Cruz. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{1}{x^{40} y^{25}}
\]
Solution
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The Deep Dive
To simplify \(\left(x^{8} y^{5}\right)^{-5}\), we apply the power of a power rule, which tells us to multiply the exponents. This leads us to: \[ \left(x^{8} y^{5}\right)^{-5} = x^{8 \cdot -5} y^{5 \cdot -5} = x^{-40} y^{-25} \] Next, we can express the negative exponents as fractions: \[ x^{-40} = \frac{1}{x^{40}} \quad \text{and} \quad y^{-25} = \frac{1}{y^{25}} \] Thus, the simplified expression becomes: \[ \frac{1}{x^{40} y^{25}} \]
