Fractional Exponents

A fractional exponent like $x^{1/n}$ means "take the $n$-th root." So $x^{1/2}$ is the square root, $x^{1/3}$ is the cube root.

For example, $16^{1/2} = 4$ because $4^2 = 16$. And $8^{1/3} = 2$ because $2^3 = 8$.

Why does this work? The power of a power rule says $(x^{1/n})^n = x^{(1/n) \times n} = x^1 = x$. That's exactly what an $n$-th root does: a number that, raised to the $n$-th power, gives you $x$.