Question
2. \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \)
Ask by Edwards Nguyen. in the Philippines
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form is \( 5x^{4}y^{2} \).
Solution
Calculate or simplify the expression \( \frac{35x^7y^8}{7(xy^2)^3} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{35x^{7}y^{8}}{7\left(xy^{2}\right)^{3}}\)
- step1: Reduce the fraction:
\(\frac{5x^{7}y^{8}}{\left(xy^{2}\right)^{3}}\)
- step2: Factor the expression:
\(\frac{5x^{7}y^{8}}{x^{3}y^{6}}\)
- step3: Reduce the fraction:
\(5x^{4}y^{2}\)
The simplified form of the expression \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \) is \( 5x^{4}y^{2} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To simplify the expression \( \frac{35 x^{7} y^{8}}{7\left(x y^{2}\right)^{3}} \), first simplify the denominator. The term \( \left(x y^{2}\right)^{3} \) can be expanded to \( x^{3} y^{6} \). Thus, the denominator becomes \( 7 x^{3} y^{6} \). Now substituting that back into the expression gives us \( \frac{35 x^{7} y^{8}}{7 x^{3} y^{6}} \). Next, divide the coefficients: \( \frac{35}{7} = 5 \). For the variables \( x \) and \( y \), apply the laws of exponents: \( x^{7}/x^{3} = x^{7-3} = x^{4} \) and \( y^{8}/y^{6} = y^{8-6} = y^{2} \). Putting it all together, the simplified result is \( 5 x^{4} y^{2} \).
