How do you multiply and simplify ${(\frac{2 x^{2}}{y^{3}})}^{3} {(\frac{y^{2}}{4 x})}^{2}$ $(\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} ( \frac { y ^ { 2} } { 4x } ) ^ { 2}$ ?

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Answer 1 · 2017-07-03T17:32:18

$\frac{x^{4}}{2 y^{5}}$ $x^4/(2y^5)$

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

Let's manage each fraction individually for now.

${(\frac{2 x^{2}}{y^{3}})}^{3} = \frac{8 x^{6}}{y^{9}}$ $(\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} =(8x^6)/y^9$

${(\frac{y^{2}}{4 x})}^{2} = \frac{y^{4}}{16 x^{2}}$ $( \frac { y ^ { 2} } { 4x } ) ^ { 2}=y^4/(16x^2)$

Now we multiply. Remember that $\frac{x^{a}}{x^{b}} = x^{a - b}$ $x^a/x^b=x^(a-b)$ .

$\frac{8 x^{6}}{y^{9}} \cdot \frac{y^{4}}{16 x^{2}} = \frac{x^{4}}{2 y^{5}}$ $(8x^6)/y^9\cdoty^4/(16x^2)=x^4/(2y^5)$

How do you multiply and simplify (2x2y3)3(y24x)2(\frac { 2x ^ { 2} } { y ^ { 3} } ) ^ { 3} ( \frac { y ^ { 2} } { 4x } ) ^ { 2}?