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Fractional exponents - this is how it was explained, basically

You know the property am * an = am+n

So a1/2 * a1/2 = a1/2+1/2 = a1 = a

Since the square root of a is a number multiplied by itself to give a, it is shown that a1/2 = √a

√a can also be written as 2√a, which can also be written 2√a1

If you notice, there is both a 1 and a 2 there, as in 1/2.

a1/3 * a1/3 * a1/3 = a1

a1/3 is multiplied by itself 3 times to get a, so it must be the cube root of a, which is written 3√a

The rule is: for fractional exponents, the denominator is the root (e.g. square root = 2, cube root = 3, etc.) and the numerator is the power (e.g. √a1)

So, 53/4 = 4√53 = 4√125

163/2 = 2√163 --by the way, 2√(163) = (2√16)3--

2√16 = 4, 43 = 64