Fractional Exponent Laws

Taking the cube root of a number or an expression is the same as raising the number or expression universally to the 1/3rd power.

So the cube root of 125x^6y^3 is the same as writing:

125^1/3 * (x^6)^1/3 * (y^3)^1/3

So essentially we have taken a root expression and offset the root itself by raising every base to the 1/3rd power.

We can simplify 125^1/3 * (x^6)^1/3 * (y^3)^1/3 by first factoring 125. 125^1/3 is 5*5*5, so we can replace 125 in our equation with 5, making our expression:

5 * (x^6)^1/3 * (y^3)^1/3

Next, we can factor x, by multiplying the exponents ^6 and ^1/3 together, which would make x equal to 2, making our expression:

5x^2(y^3)^1/3

Now, lastly, we factor out variable y by doing the same as we did for x, and multiplying the exponents ^3 and ^1/3 together, which would be equal to 1, making our expression:

5x^2y

That's it!