How do you simplify #((\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

#color(indigo)(=>(2x^8)/(9y^6)#

Law of Indices :

#color(crimson)(a^m * a^n = a^(m+n)#

#color(crimson)((a^m)^n = a^(mn)#

#color(crimson)((a^m)/(a^n) = a^(m-n)#

Given : #((2x^3)/(x^2y^4))^3* ((xy^2)^5/(6y^2)^2)#

#=>((2x)/(y^4))^3*((x^5y^(10))/(36y^4))#

#=> ((8x^3)/y^(12)) * ((x^5y^6)/36)#

#=> (8x^3*x^5*y^6) / (36y^(12))#

#color(indigo)(=>(2x^8)/(9y^6)#