Question
Simplify \( \frac{5 x^{-2}}{3 x} \cdot \frac{2 y^{3}}{x^{10}} \) \( \frac{[?] y[]}{[] x[]} \)
Ask by Powers West. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{10y^{3}}{3x^{13}} \).
Solution
Calculate or simplify the expression \( (5*x^(-2))/(3*x) * (2*y^3)/(x^10) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\frac{\left(5x^{-2}\right)}{\left(3x\right)}\times \left(2y^{3}\right)}{\left(x^{10}\right)}\)
- step1: Evaluate:
\(\frac{\frac{\left(5x^{-2}\right)}{3x}\times 2y^{3}}{x^{10}}\)
- step2: Remove the parentheses:
\(\frac{\frac{5x^{-2}}{3x}\times 2y^{3}}{x^{10}}\)
- step3: Reduce the fraction:
\(\frac{\frac{5}{3x^{3}}\times 2y^{3}}{x^{10}}\)
- step4: Multiply the terms:
\(\frac{\frac{10y^{3}}{3x^{3}}}{x^{10}}\)
- step5: Multiply by the reciprocal:
\(\frac{10y^{3}}{3x^{3}}\times \frac{1}{x^{10}}\)
- step6: Multiply the terms:
\(\frac{10y^{3}}{3x^{3}\times x^{10}}\)
- step7: Multiply the terms:
\(\frac{10y^{3}}{3x^{13}}\)
The simplified expression is \( \frac{10y^{3}}{3x^{13}} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression, we start by rewriting it: \[ \frac{5 x^{-2}}{3 x} \cdot \frac{2 y^{3}}{x^{10}} = \frac{5 \cdot 2 \cdot x^{-2} \cdot y^{3}}{3 \cdot x \cdot x^{10}} = \frac{10 y^{3} x^{-2}}{3 x^{11}} \] Now, combine and simplify the \(x\) terms: \[ = \frac{10 y^{3}}{3 x^{11 + 2}} = \frac{10 y^{3}}{3 x^{13}} \] So, the final simplified form is: \[ \frac{10 y^{3}}{3 x^{13}} \] The expression can be represented as \( \frac{10 y^{3}}{3 x^{13}} \).
