Question
Simplify the expression completely: \( \frac{32 x^{11} y^{10}}{15 x^{6} y^{8}} \) Use the preview button to check your answer before you submit it. Answer \( = \)
Ask by Crawford Cruz. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{32x^5y^2}{15}
\]
Solution
\[
\frac{32 x^{11} y^{10}}{15 x^{6} y^{8}} = \frac{32}{15} \cdot x^{11-6} \cdot y^{10-8} = \frac{32}{15} \cdot x^5 \cdot y^2
\]
Answer \( = \frac{32x^5y^2}{15} \)
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Simplify this solution The Deep Dive
To simplify the expression \( \frac{32 x^{11} y^{10}}{15 x^{6} y^{8}} \), we can start by separating the coefficients and the variables. 1. **Coefficients**: \( \frac{32}{15} \) remains as is because 32 and 15 have no common factors. 2. **For \( x \)**: We apply the laws of exponents: \( x^{11}/x^{6} = x^{11-6} = x^{5} \). 3. **For \( y \)**: Similarly, \( y^{10}/y^{8} = y^{10-8} = y^{2} \). Combining these results, we get: \[ \frac{32}{15} x^{5} y^{2} \] So, the fully simplified expression is \( \frac{32 x^{5} y^{2}}{15} \). Answer \( = \frac{32 x^{5} y^{2}}{15} \)
