What is ((4x^2)/(8y^3))^2 ?

The solution to ((4x^2)/(8y^3))^2 is (x^4)/(4y^6)

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simplify ((4x^2)/(8y^3))^2

simplify

(\frac{4 x ^{2}}{8 y ^{3}})^{2}

\frac{x ^{4}}{4 y ^{6}}

Solution steps

(\frac{4 x ^{2}}{8 y ^{3}})^{2}

Apply exponent rule:

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

= \frac{( 4 x ^{2} ) ^{2}}{( 8 y ^{3} ) ^{2}}

Simplify

(4 x^{2})^{2} : 16 x^{4}

= \frac{16 x ^{4}}{( 8 y ^{3} ) ^{2}}

Simplify

(8 y^{3})^{2} : 64 y^{6}

= \frac{16 x ^{4}}{64 y ^{6}}

Cancel the common factor:

16

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

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

(x - 2) (3 x + 4)

(2 + 1) (2 - 1)

\frac{\frac{x ^{2} - 81}{x ^{2} - x - 72}}{\frac{x - 2}{x + 8}}

6 y (2 - y)