How do you simplify $({(\frac{2 x^{3}}{x^{2} y^{4}})}^{3}) (\frac{{(x y^{2})}^{5}}{{(6 y^{2})}^{2}})$ $((\frac { 2x ^ { 3} } { x ^ { 2} y ^ { 4} } ) ^ { 3} )(\frac { ( x y ^ { 2} ) ^ { 5} } { ( 6y ^ { 2} ) ^ { 2} })$ ?

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Answer 1 · 2018-05-19T11:38:20

$\Rightarrow \frac{2 x^{8}}{9 y^{6}}$ $color(indigo)(=>(2x^8)/(9y^6)$

Law of Indices :

$a^{m} \cdot a^{n} = a^{m + n}$ $color(crimson)(a^m * a^n = a^(m+n)$

${(a^{m})}^{n} = a^{m n}$ $color(crimson)((a^m)^n = a^(mn)$

$\frac{a^{m}}{a^{n}} = a^{m - n}$ $color(crimson)((a^m)/(a^n) = a^(m-n)$

Given : ${(\frac{2 x^{3}}{x^{2} y^{4}})}^{3} \cdot ⎛ ⎝ \frac{{(x y^{2})}^{5}}{{(6 y^{2})}^{2}} ⎞ ⎠$ $((2x^3)/(x^2y^4))^3* ((xy^2)^5/(6y^2)^2)$

$\Rightarrow {(\frac{2 x}{y^{4}})}^{3} \cdot (\frac{x^{5} y^{10}}{36 y^{4}})$ $=>((2x)/(y^4))^3*((x^5y^(10))/(36y^4))$

$\Rightarrow (\frac{8 x^{3}}{y^{12}}) \cdot (\frac{x^{5} y^{6}}{36})$ $=> ((8x^3)/y^(12)) * ((x^5y^6)/36)$

$\Rightarrow \frac{8 x^{3} \cdot x^{5} \cdot y^{6}}{36 y^{12}}$ $=> (8x^3*x^5*y^6) / (36y^(12))$

$\Rightarrow \frac{2 x^{8}}{9 y^{6}}$ $color(indigo)(=>(2x^8)/(9y^6)$

How do you simplify ((2x3x2y4)3)((xy2)5(6y2)2)((\frac { 2x ^ { 3} } { x ^ { 2} y ^ { 4} } ) ^ { 3} )(\frac { ( x y ^ { 2} ) ^ { 5} } { ( 6y ^ { 2} ) ^ { 2} })?