Question

Solve it by exponent principal?

Answer 1

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)`