Question

Simplify: 9^1/3*27^-1/2/3^1/6*3^-2/3​

Answer 1

Step-by-step explanation:

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#