How do you simplify #(4/81)^(3/2)#?

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Answer 1 · 2016-10-05T09:28:09

#(4/81)^(3/2)=8/729#

We use here the identities #(a/b)^m=a^m/b^m# and #(a^m)^n=a^((mxxn))#

Hence #(4/81)^(3/2)#

= #((2xx2)/(3xx3xx3xx3))^(3/2)#

= #(2^2/3^4)^(3/2)#

= #(2^2)^(3/2)/(3^4)^(3/2)# - using #(a/b)^m=a^m/b^m#

= #2^((2xx3/2))/(3^((4xx3/2))# - using #(a^m)^n=a^((mxxn))#

= #2^3/3^6#

= #(2xx2xx2)/(3xx3xx3xx3xx3xx3)#

= #8/729#