[9^(1/3)] x [27^(-1/2)] all divided by [3^(-1/6)] x [3^(-2/3)] ?

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Answer 1 · 2018-02-10T01:00:49

The answer is #1#.

Change all the numbers to a common base of #3#, then apply the exponent addition rule:

#\qquad\quad(9^(1/3)*27^(-1/2))/(3^(-1/6)*3^(-2/3))#

#=((3^2)^(1/3)*(3^3)^(-1/2))/(3^(-1/6)*3^(-2/3))#

#=(3^(2/3)*3^(-3/2))/(3^(-1/6)*3^(-2/3))#

#=(3^(2/3-3/2))/(3^(-1/6-2/3))#

#=(3^(4/6-9/6))/(3^(-1/6-4/6))#

#=(3^(-5/6))/(3^(-5/6))#

#=3^(-5/6)*3^(5/6)#

#=3^(-5/6+5/6)#

#=3^0#

#=1#