1
Solved example of quotient of powers
$\frac{\left(x^{\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$
$\frac{\left(y^{\frac{3}{2}}\sqrt[5]{x}\right)^{10}}{\left(y^{-\frac{2}{5}}x^{\frac{2}{3}}\right)^5}$
3
Multiplying the fraction and term
$\frac{\left(\sqrt[5]{x}\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$
4
The power of a product is equal to the product of it's factors raised to the same power
$\frac{\left(\sqrt[5]{x}\right)^{10}\left(\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$
5
Applying the power of a power property
$\frac{x^{2}\left(\sqrt{y^{3}}\right)^{10}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$
6
Applying the power of a power property
$\frac{x^{2}y^{15}}{\left(y^{-\frac{2}{5}}\sqrt[3]{x^{2}}\right)^5}$
7
The power of a product is equal to the product of it's factors raised to the same power
$\frac{x^{2}y^{15}}{\left(y^{-\frac{2}{5}}\right)^5\left(\sqrt[3]{x^{2}}\right)^5}$
8
Applying the power of a power property
$\frac{x^{2}y^{15}}{y^{-2}\left(\sqrt[3]{x^{2}}\right)^5}$
9
Simplify the fraction by $y$
$\frac{x^{2}y^{17}}{\left(\sqrt[3]{x^{2}}\right)^5}$
10
Applying the power of a power property
$\frac{x^{2}y^{17}}{\sqrt[3]{x^{10}}}$
11
Simplify the fraction by $x$
$\frac{y^{17}}{\sqrt[3]{x^{4}}}$
Answer
$\frac{y^{17}}{\sqrt[3]{x^{4}}}$