Use rational exponents to simplify the radical. If rational exponents appear after simplifying, write the answer in radical notation.

20sqrt(x^12)

well, the sqrt x^12= x^6

10x^6

To simplify the given radical expression using rational exponents, we can rewrite the square root as x^(1/2):

20sqrt(x^12) = 20(x^12)^(1/2)

Now, we can apply the power rule of exponents, which states that (a^m)^n = a^(m*n):

20(x^12)^(1/2) = 20(x^(12*(1/2)))

Simplifying the exponent:

20(x^12)^(1/2) = 20(x^6)

Finally, we can write the answer in radical notation:

20sqrt(x^12) = 20(x^6)