Solve it by exponent principal?

enter image source here

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)

Related questions
Impact of this question
1117 views around the world
You can reuse this answer
Creative Commons License