How do you evaluate #x^ { - 2} [ x ^ { 6} [ x ( x ^ { - 3} ) ^ { \frac { 1} { 3} } ] ^ { \frac { 1} { 9} } \} ^ { \frac { 2} { 3} }#?

1 Answer
Nityananda
Feb 1, 2018

#x^2#

Explanation:

Given, #x^-2[x^6{x(x^-3)^(1/3)}^(1/9)]^(2/3)#
#rArr x^-2[x^6{x^1(x^-3)^(1/3)}^(1/9)]^(2/3)#
#rArr x^-2[x^6{x^1x^-1}^(1/9)]^(2/3)#
#rArr x^-2[x^6{x^(1-1)}^(1/9)]^(2/3)#
#rArr x^-2[x^6{x^0}^(1/9)]^(2/3)#
#rArr x^-2[x^6{1}^(1/9)]^(2/3)#
#rArr x^-2[x^6 *1]^(2/3)#
#rArr x^-2 x^(6*2/3)#
#rArr x^-2 x^4#
#rArr x^(-2+4)#
#rArr x^2#

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