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)