Step-by-step Solution

Simplify the quotient of powers $\frac{\left(x^{-\frac{1}{5}}y^{\frac{3}{2}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$

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Step-by-step Solution

Problem to solve:

$\frac{\left(x^{\left(-1\right)\cdot\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$

Solving method

Learn how to solve quotient of powers problems step by step online.

$\frac{\left(x^{-\frac{1}{5}}\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$

Unlock this full step-by-step solution!

Learn how to solve quotient of powers problems step by step online. Simplify the quotient of powers ((x^(-0.2)y^(3/2))^10)/((y^(-0.4)x^0.6666666666666666)^5). Divide 3 by 2. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. Applying the power of a power property.

Final Answer

$\frac{y^{17}}{\sqrt[3]{x^{16}}}$
$\frac{\left(x^{\left(-1\right)\cdot\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$

Main topic:

Quotient of powers

Time to solve it:

~ 0.04 s