Laws of Indices Part 2: Negatives and Fractions | Algebra Maths FuseSchool

In this video we are going to look at what happens with negative indices and fractional indices. You should already know the other 4 ‘Laws of Indices’ but if you have forgotten, have a look at them first. For negative indices, we drop whatever numbers and/or letters have the negative indice (also known as power or exponent) down to the denominator and make the indice (power or exponent) positive. E.g. x^(-2) is the same as 1/x^2 where it was negative when a numerator and becomes positive as a denominator. Fractional indices: an indice of a 1/2 is the same as square root. An indice of 1/3 is the same as cube root. An indice of 1/4 is the same as 4 root. But what if the numerator isn’t one? An indice of 3/2 means square root the number and then cube it. An indice of 2/3 means to cube root and then square it. So the denominator is still the root of the number, and the numerator then raises the root to the power. Fractional law of indices = power / root. Power makes things bigger so is on top, and root makes things smaller so is on the bottom. I always do the root first and then the power second to keep the numbers small, but you can actually do them in either order. Although I really recommend rooting first and doing the power second. Some examples: 25^3/2 means to square root 25 and then cube the answer. 25^3/2 = 5^3 = 125.

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