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

The solution to (y/x)^2(3/(4xy))^3 is (27)/(64yx^5)

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

simplify

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

\frac{27}{64 y x ^{5}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(\frac{3}{4 x y})^{3} : \frac{27}{64 x ^{3} y ^{3}}

= \frac{y ^{2}}{x ^{2}} \cdot \frac{27}{64 x ^{3} y ^{3}}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{y ^{2} \cdot 27}{x ^{2} \cdot 64 x ^{3} y ^{3}}

Simplify

\frac{y ^{2}}{y ^{3}} : \frac{1}{y}

= \frac{27}{x ^{2} \cdot 64 x ^{3} y}

Simplify

x^{2} x^{3} : x^{5}

= \frac{27}{x ^{5} \cdot 64 y}

= \frac{27}{64 x ^{5} y}

= \frac{27}{64 y x ^{5}}

f (x) = \frac{cos ( x )}{x ^{\frac{1}{3}}}

\frac{( 12 x ^{5} y ^{4} )}{( 2 x ^{3} \cdot y )}

(2 m - n)^{3} + (2 m + n)^{3} + 12 m (4 m^{2} - n^{2})

a^{2} - 1 + 2 b - b^{2}

\frac{3}{5} + \frac{8}{b} + \frac{4}{2}

What is (y/x)^2(3/(4xy))^3 ?
The solution to (y/x)^2(3/(4xy))^3 is (27)/(64yx^5)