Question

I want to know how to simplify it

Answer 1

`(2)/(3)`

Explanation:

`\sqrt[4]{(16)/(81) }`

Firstly, we want to get rid of the '
`\sqrt[4]{}`'. One way to get rid of a root is by apply the rule
`\sqrt[n]{x^(n) } =x`. If we could represent the term inside the root in index form to the power of 4, we could cancel out the '
`\sqrt[4]{}`'.

So let's try represent the terms in the fraction in index form to the power of 4. It may be helpful to recall the rule
`(x^(m))^(n)=x^(mn)`.

`16=4^(2)= (2^(2))^(2) =2^(4)`

`81=9^(2)=(3^(2))^(2)=3^(4)`

So now we can rewrite
`\sqrt[4]{(16)/(81) }` as
`\sqrt[4]{(2^(4) )/(3^(4) ) }` or
`\sqrt[4]{((2)/(3) )^(4) }`. Now we can canel the power of 4 and the '
`\sqrt[4]{}`' to get:
`(2)/(3)`

Answer 2

Explanation:

you have to take one prpblem to answer the other