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 Turner Tucker. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2x^{3} y^{-4} \)
Solution
To simplify the expression \( \frac{110 x^{5} y^{3}}{55 x^{2} y^{7}} \) and express the answer in exponent form, follow these steps:
1. **Simplify the Coefficients:**
\[
\frac{110}{55} = 2
\]
2. **Simplify the \(x\)-Terms:**
\[
\frac{x^{5}}{x^{2}} = x^{5-2} = x^{3}
\]
3. **Simplify the \(y\)-Terms:**
\[
\frac{y^{3}}{y^{7}} = y^{3-7} = y^{-4}
\]
4. **Combine All Parts:**
\[
2 \cdot x^{3} \cdot y^{-4} = 2x^{3}y^{-4}
\]
**Final Answer:**
\[
2x^{3} y^{-4}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the division of the expression \( \frac{110 x^{5} y^{3}}{55 x^{2} y^{7}} \), we start by simplifying the coefficients and the variables separately. First, divide the coefficients: \( \frac{110}{55} = 2 \). Next, for \( x \) terms, use the rule of exponents \( \frac{x^m}{x^n} = x^{m-n} \): \( \frac{x^{5}}{x^{2}} = x^{5-2} = x^{3} \). Then, for the \( y \) terms: \( \frac{y^{3}}{y^{7}} = y^{3-7} = y^{-4} \). Putting it all together, we have: \( 2 x^{3} y^{-4} \). Thus, the final answer in exponent form is \( \mathbf{2 x^{3} y^{-4}} \).
