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