Simplify the quotient of powers ((4xy^4z^(-2))^2)/(2x^4y^3z^(-2))

 Exercise

$\frac{\left(4xy^{4}z^{-2}\right)^{2}}{2x^{4}y^{3}z^{-2}}$

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

$\frac{16x^2y^{8}z^{-4}}{2x^4y^3z^{-2}}$

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Simplify the fraction $\frac{16x^2y^{8}z^{-4}}{2x^4y^3z^{-2}}$ by $y$

$\frac{16x^2y^{5}z^{-4}}{2x^4z^{-2}}$

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Simplify the fraction by $x$

$\frac{16y^{5}z^{-4}}{2x^{2}z^{-2}}$

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Simplify the fraction by $z$

$\frac{16y^{5}}{2x^{2}z^{2}}$

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Cancel the fraction's common factor $2$

$\frac{8y^{5}}{x^{2}z^{2}}$

$\frac{8y^{5}}{x^{2}z^{2}}$

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