Question

How do you simplify `root4(x^12/y^4)`?

Answer 1

`root4(x^12/y^4) = x^3/y`

Explanation:

`root4(x^12/y^4) = (x^12/y^4)^(1/4) =(x^12 * y^-4)^(1/4)`

Remember the rule of indices: `(a^m)^n = a^(m xx n)`

Applying this rule to the expression:

`(x^12 * y^-4)^(1/4) = x^(12/4) * y^(-4/4)`

`= x^3 * y^-1`

`= x^3/y`

Answer 2

Detailed explanation:

Explanation:

`color(blue)(root(4)((x^12)/(y^4))`

Let's solve it using simple steps

First we should know that `color(brown)(root(x)(y/z)=(root(x)(y))/(root(x)(z))`

So,

`rarrroot(4)((x^12)/(y^4))=(root(4)(x^12))/(root(4)(y^4))`

Now solve `root(4)(x^12)` and `root(4)(y^4)` each independantly

Let's solve `root(4)(x^12)` (expand it)

`rarrroot(4)(x^12)=root(4)(x*x*x*x*x*x*x*x*x*x*x*x)`

Take out the roots

`rarrroot(4)(underbrace(x*x*x*x)*underbrace(x*x*x*x)*underbrace(x*x*x*x))`

`rarrx*x*x`

`color(green)(rArrx^3`

Now solve `root(4)(y^4)` (expand it)

`rarrroot(4)(y^4)=root(4)(y*y*y*y)`

Take out the roots

`rarrroot(4)(underbrace(y*y*y*y))`

`color(green)(rArry`

So, put the solutions together to get our answer

`color(blue)(x^3/y`

Hope this helps! :)