Quotient of powers Calculator
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$\left(\frac{4}{3} x^2 y^3\right)^3\left(\frac{3}{16x^5}\right)^2$
$\left(\frac{3}{16x^5}\right)^2\left(\frac{4}{3}y^3x^2\right)^3$
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 $16$ from the fraction's denominator
$\frac{64}{27}\left(\frac{1}{16}\cdot\frac{3}{x^5}\right)^2y^{9}x^{6}$
6
The power of a product is equal to the product of it's factors raised to the same power
$\frac{64}{27}\cdot \frac{1}{256}y^{9}x^{6}\left(\frac{3}{x^5}\right)^2$
7
Multiply $\frac{1}{256}$ times $\frac{64}{27}$
$\frac{1}{108}y^{9}x^{6}\left(\frac{3}{x^5}\right)^2$
8
The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
$\frac{1}{108}y^{9}x^{6}\cdot\frac{9}{x^{10}}$
9
Multiplying the fraction and term
$\frac{\frac{1}{12}y^{9}x^{6}}{x^{10}}$