simplify ^5 square root x^20

the fifth-root of x^20 is

(x^20)^(1/5) = x^(20 * 1/5) = x^4

Because (x^4)^5 = x^20

Roots are just fractional powers.

Thank you very much!!!

To simplify the expression ^5√(x^20), we need to apply the properties of exponents and radicals.

First, we can rewrite x^20 as (x^4)^5. This uses the property that (a^m)^n = a^(m*n).

So, the expression becomes ^5√((x^4)^5).

Now, we can simplify the expression by applying the power rule of radicals. The power rule states that ^n√(a^m) = a^(m/n).

Using this rule, we can rewrite the expression as (x^4)^(5/5).

Simplifying further, (x^4)^(5/5) = x^(4*(5/5)) = x^4.

Therefore, the simplified form of ^5√(x^20) is x^4.