Exponent Laws

The laws governing the combination of Exponents (Powers) are

$$x^m\cdot x^n = x^{m+n}$$ (1)

$${x^m\over x^n} = x^{m-n}$$ (2)

$$(x^m)^n = x^{mn}$$ (3)

$$(xy)^m = x^m y^m$$ (4)

$$\left({x\over y}\right)^n = {x^n\over y^n}$$ (5)

$$x^{-n} = {1\over x^n}$$ (6)

$$\left({x\over y}\right)^{-n} = \left({y\over x}\right)^n,$$ (7)

where quantities in the Denominator are taken to be nonzero. Special cases include

$$x^1=x$$ (8)

and

$$x^0=1$$ (9)

for $x\not=0$. The definition $0^0=1$ is sometimes used to simplify formulas, but it should be kept in mind that this equality is a definition and not a fundamental mathematical truth.

See also Exponent, Power