Laws of Indices

Sometimes called the "Laws of Exponents" (also called "Rules of Exponents") come from three ideas:

The exponent says how many times to use the number in a multiplication.

A negative exponent means divide, because the opposite of multiplying is dividing

A fractional exponent like 1/n means to take the nth root:

Laws of Exponents

Here are the Laws (for more detailed explanations follow this link to the maths is fun site):

Law	Example
x¹ = x	6¹ = 6
x⁰ = 1	7⁰ = 1
x^-1 = 1/x	4^-1 = 1/4

x^mxⁿ = x^m⁺ⁿ	x²x³ = x²⁺³ = x⁵
x^m/xⁿ = x^m-n	x⁶/x² = x^6-2 = x⁴
(x^m)ⁿ = x^mn	(x²)³ = x²^×3 = x⁶
(xy)ⁿ = xⁿyⁿ	(xy)³ = x³y³
(x/y)ⁿ = xⁿ/yⁿ	(x/y)2 = x2 / y2
x^-n = 1/xⁿ	x^-3 = 1/x³
And the law about Fractional Exponents: