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Quotient of powers Calculator

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1

Solved example of quotient of powers

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

Divide $1$ by $5$

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

$\frac{y^{17}}{\sqrt[3]{x^{4}}}$

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