Question
Divide. Leave your answer in exponent form. Assume that all variables in any denominator are nonzero. \( \frac{110 x^{5} y^{3}}{55 x^{2} y^{7}} \)
Ask by Adkins Dunn. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2x^{3} y^{-4} \)
Solution
To simplify the expression \( \frac{110 x^{5} y^{3}}{55 x^{2} y^{7}} \), follow these steps:
1. **Divide the coefficients:**
\[
\frac{110}{55} = 2
\]
2. **Divide the \(x\)-terms using the laws of exponents (\(x^a / x^b = x^{a-b}\)):**
\[
\frac{x^{5}}{x^{2}} = x^{5-2} = x^{3}
\]
3. **Divide the \(y\)-terms using the laws of exponents (\(y^a / y^b = y^{a-b}\)):**
\[
\frac{y^{3}}{y^{7}} = y^{3-7} = y^{-4}
\]
Putting it all together:
\[
2x^{3}y^{-4}
\]
**Final Answer:**
\[
2x^{3} y^{-4}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To divide the coefficients, we have \( \frac{110}{55} = 2 \). For the variables, we apply the rule of exponents: subtract the exponent in the denominator from the exponent in the numerator. For \( x \), we calculate \( x^{5 - 2} = x^{3} \). For \( y \), we find \( y^{3 - 7} = y^{-4} \). Putting it all together, the expression simplifies to \( 2x^{3}y^{-4} \). Now, in exponent form, we typically leave negative exponents in the denominator: The final answer is \( \frac{2x^{3}}{y^{4}} \).
