# Laws of Exponents

Laws of Exponents

The laws of exponents show the power of elementary algebra and lay the groundwork for logarithms. The laws are:

m

a

n

a

m+n

a

m

a

n

a

m-n

a

n

()

m

a

mn

a

m

(ab)

m

a

n

b

m

a

b

m

a

m

b

0

a

-1

a

1

a

-m

a

1

m

a

1

m

a

m

a

This Demonstration does not prove the first five of these laws; for a proof, you need to use mathematical induction.