How do you multiply #(x ^ { 4} y ^ { 2} ) ^ { 2} * \root[ 3] { x ^ { 3} }#?

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Answer 1 · 2018-01-25T15:28:06

#color(blue)((x ^ { 4} y ^ { 2} ) ^ { 2} * \root[ 3] { x ^ { 3} } = (x^9y^4)#

Given:

#color(blue)((x ^ { 4} y ^ { 2} ) ^ { 2} * \root[ 3] { x ^ { 3} }#

#rArr (x^4)^2*(y^2)^2*(x^3)^(1/3)#

#rArr (x^8)*(y^4)*x^(3(1/3)#

#rArr (x^8)*(y^4)*x^( 3/3)#

#rArr x^8*y^4*x^1#

#rArr x^9*y^4#

Hence,

#color(blue)((x ^ { 4} y ^ { 2} ) ^ { 2} * \root[ 3] { x ^ { 3} } = (x^9y^4)#