Concepts Simplified: Fractional Exponents

What Does $9^{1/2}$ Mean?

The exponent $1/2$ means you’re taking the square root:
$$9^{1/2} = \sqrt{9} = 3$$

Why Is That True?

Because:
$$(9^{1/2})^2 = 9^{(1/2 \times 2)} = 9^1 = 9$$
So, you're finding a number that, when squared, gives 9 — and that's 3.

General Rule

$$a^{1/n} = \sqrt[n]{a}$$
Examples:
$$a^{1/2} = \sqrt{a}$$
$$a^{1/3} = \sqrt[3]{a}$$
$$a^{m/n} = \sqrt[n]{a^m}$$

Another Example

$$27^{1/3} = \sqrt[3]{27} = 3$$
Because $3 \times 3 \times 3 = 27$