Question
Multiply the rational expressions. \( \frac{4 x^{2} y^{9}}{12 x y^{8}} \cdot \frac{6 x^{2}}{32 y^{2}}=\square \quad \frac{\square}{\square} \square^{\square} \)
Ask by Simpson Young. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The product of the rational expressions is \( \frac{x^{3}}{16y} \).
Solution
Calculate or simplify the expression \( \frac{4x^2y^9}{12xy^8} \cdot \frac{6x^2}{32y^2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{4x^{2}y^{9}}{12xy^{8}}\times \frac{6x^{2}}{32y^{2}}\)
- step1: Divide the terms:
\(\frac{xy}{3}\times \frac{6x^{2}}{32y^{2}}\)
- step2: Calculate:
\(\frac{xy}{3}\times \frac{3x^{2}}{16y^{2}}\)
- step3: Reduce the fraction:
\(x\times \frac{x^{2}}{16y}\)
- step4: Multiply the terms:
\(\frac{x\times x^{2}}{16y}\)
- step5: Multiply the terms:
\(\frac{x^{3}}{16y}\)
The product of the given rational expressions is \( \frac{x^{3}}{16y} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To multiply the rational expressions, first, simplify each expression before multiplying. The first fraction simplifies as follows: \( \frac{4x^2y^9}{12xy^8} = \frac{4}{12} \cdot \frac{x^2}{x} \cdot \frac{y^9}{y^8} = \frac{1}{3} \cdot x \cdot y = \frac{xy}{3} \). For the second fraction: \( \frac{6x^2}{32y^2} = \frac{6}{32} \cdot \frac{x^2}{1} \cdot \frac{1}{y^2} = \frac{3}{16} \cdot x^2 = \frac{3x^2}{16} \). Now, multiply the two simplified fractions: \[ \frac{xy}{3} \cdot \frac{3x^2}{16} = \frac{xy \cdot 3x^2}{3 \cdot 16} = \frac{3x^3y}{48} = \frac{x^3y}{16}. \] Thus, the answer is: \(\frac{x^3y}{16}\).
