Exponents are used to show how many times a base value is multiplied by itself. This simplifies equations to an easier-to-read format.

Exponent Laws

There are seven basic rules that explain how to solve most math equations that involve exponents.

The exponent rules are:

Product of powers rule — Add powers together when multiplying like bases.

a^m × aⁿ = a^m+n

Quotient of powers rule — Subtract powers when dividing like bases.

 a^m/aⁿ = a^m-n

Power of powers rule — Multiply powers together when raising a power by another exponent.

(a^m)ⁿ = a^mn

Power of a product rule — Distribute power to each base when raising several variables by a power.

(ab)^m = a^mb^m

Power of quotient rule — Distribute power to all values in a quotient.

(a/b)^m = a^m/b^m

Zero power rule — Any base raised to the power of zero becomes one.

a⁰ = 1

One Rule — Any number or variable that has the exponent of 1 is equal to the number or variable itself.

a¹ = a,

7¹ = 1

Negative exponent rule — To change a negative exponent to a positive one, flip it into a reciprocal.

a^-m = 1/a^m