What is ((4xy^3)/(x^2))^2 ?

The solution to ((4xy^3)/(x^2))^2 is (16y^6)/(x^2)

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simplify ((4xy^3)/(x^2))^2

simplify

(\frac{4 x y ^{3}}{x ^{2}})^{2}

\frac{16 y ^{6}}{x ^{2}}

Solution steps

(\frac{4 x y ^{3}}{x ^{2}})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 4 x y ^{3} ) ^{2}}{( x ^{2} ) ^{2}}

Simplify

(4 x y^{3})^{2} : 16 x^{2} y^{6}

= \frac{16 x ^{2} y ^{6}}{( x ^{2} ) ^{2}}

Simplify

(x^{2})^{2} : x^{4}

= \frac{16 x ^{2} y ^{6}}{x ^{4}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{x ^{2}}{x ^{4}} = \frac{1}{x ^{4 - 2}}

= \frac{16 y ^{6}}{x ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

= \frac{16 y ^{6}}{x ^{2}}

2 q^{2} - 8

\frac{- 9}{( - 27 )}

(\frac{1}{3})^{12}

\frac{- 5 q ^{- 4}}{( - 5 q ^{4} ) ^{2}}

2 x b^{2} - 5 b x