# Quotient of powers Calculator

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### Difficult Problems

1

Example

$\left(\frac{4}{3} x^2 y^3\right)^3\left(\frac{3}{16x^5}\right)^2$
2

Divide $4$ by $3$

$\left(\frac{3}{16x^5}\right)^2\left(\frac{4}{3}y^3x^2\right)^3$
3

The power of a product is equal to the product of it's factors raised to the same power

$\frac{64}{27}\left(\frac{3}{16x^5}\right)^2\left(y^3\right)^3x^{6}$
4

Applying the power of a power property

$\frac{64}{27}\left(\frac{3}{16x^5}\right)^2y^{9}x^{6}$
5

Taking out the constant $1$ from the fraction's denominator

$\frac{64}{27}\left(\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{1}{16}\cdot\frac{3}{x^5}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}}{16}\right)^2y^{9}x^{6}$
6

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\frac{64}{27}\cdot\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\left(\frac{1}{16}\cdot\frac{3}{x^5}\right)^2}{256}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}}{16^2}y^{9}x^{6}$

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