How do you simplify #(\root [ 11] { 9x ^ { 6} y } ) ^ { 7}#?

1 Answer
Apr 20, 2018

Answer:

#" "#
#color(brown)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}= [9^(7/11)][x^(42/11)][y^(7/11)]#

Explanation:

#" "#
We have #color(red)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}#

Useful Exponent formula:

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

#color(blue)(root(n)m = m^(1/n)#

#color(blue)(root(n)(a^m) = a^(m/n)#

Consider:

#(\root [ 11] { 9x ^ { 6} y } ) ^ { 7}# given expression

Simplify this expression using the formula list above.

#[root(11)(9)*root(11)(x^6)*root(11)(y)]^7#

#rArr [root(11)(9^1)*root(11)(x^6)*root(11)(y^1)]^7#

#rArr [9^(1/11)*x^(6/11)*y^(1/11)]^7#

#rArr 9^(7/11)*x^(42/11)*y^(7/11)#

Hence,

#color(brown)((\root [ 11] { 9x ^ { 6} y } ) ^ { 7}= [9^(7/11)][x^(42/11)][y^(7/11)]#

Hope it helps.