Question
Simplify the expression. Write the result using positive exponents only. \[ \left(\frac{x^{-4} y^{4}}{x^{3} y^{8}}\right)^{3} \]
Ask by Daniels Coleman. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{1}{x^{21} y^{12}}
\]
Solution
To simplify the expression \(\left(\frac{x^{-4} y^{4}}{x^{3} y^{8}}\right)^{3}\) and express it with positive exponents, follow these steps:
1. **Simplify the Inside of the Parentheses:**
\[
\frac{x^{-4} y^{4}}{x^{3} y^{8}} = x^{-4 - 3} \cdot y^{4 - 8} = x^{-7} y^{-4}
\]
2. **Apply the Exponent Outside the Parentheses:**
\[
\left(x^{-7} y^{-4}\right)^3 = x^{-21} y^{-12}
\]
3. **Rewrite with Positive Exponents:**
\[
x^{-21} y^{-12} = \frac{1}{x^{21} y^{12}}
\]
So, the simplified expression with positive exponents is:
\[
\frac{1}{x^{21} y^{12}}
\]
**Answer:**
\[\frac{1}{\,x^{21}\, y^{12}\,}\]
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Simplify this solution Mind Expander
To simplify the expression \(\left(\frac{x^{-4} y^{4}}{x^{3} y^{8}}\right)^{3}\), we first simplify the inner fraction: \[ \frac{x^{-4} y^{4}}{x^{3} y^{8}} = x^{-4 - 3} y^{4 - 8} = x^{-7} y^{-4} \] Next, we raise this result to the power of 3: \[ \left(x^{-7} y^{-4}\right)^{3} = x^{-7 \cdot 3} y^{-4 \cdot 3} = x^{-21} y^{-12} \] Finally, we rewrite the expression using positive exponents: \[ \frac{1}{x^{21} y^{12}} \] Thus, the simplified expression with positive exponents is: \[ \frac{1}{x^{21} y^{12}} \]
