Solve it by exponent principal?

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1 Answer
F. Javier B.
May 19, 2018

Factorize numbers and use power rules:

#243=3^5#
#32=2^5#
#196=2^2·7^2#

With this, expresion result in #((3^5)^(-2/3)·(2^5)^(-1/5))/((2^2·7^2)^(1/2))^(-1)=#

#=(3^(-10/3)·cancel2^(-5/5))/(cancel2^(-1)·7^(-1))=7/3^(10/3)#

Now #3^(10/3)=root(3)(3^10)=root(3)(3^3·3^3·3^3·3)=27root(3)3#

Finally we have #7/3^(10/3)=7/(27root(3)3)#

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