Exponent Rules

See how to use the exponent rules
to simplify the exponents.
15 examples and their solutions.

a^m⋅aⁿ = a^{m + n}
(a^m)ⁿ = a^m⋅n
(ab)^m = a^m⋅b^m
a^maⁿ = a^{m - n}
(ab)^m = a^mb^m
a⁰ = 1
a^-m = 1a^m

a^m⋅aⁿ

Formula

a^m⋅aⁿ = a^{m + n}

Example

x⁶⋅x⁸

Solution

Example

3²xy⁴⋅3x³y⁷

Solution

(a^m)ⁿ

Formula

(a^m)ⁿ = a^m⋅n

Example

(x²)³

Solution

Example

((x⁴)²)⁵

Solution

(ab)^m

Formula

(ab)^m = a^m⋅b^m

Example

(x³y)²

Solution

a^maⁿ

Formula

a^maⁿ = a^{m - n}

Example

x⁸x³ = ? (x ≠ 0)

Solution

Example

12x⁷y²z⁹4x⁴y²z⁵ = ? (x, y, z ≠ 0)

Solution

(ab)^m

Formula

(ab)^m = a^mb^m

Example

(xy²)³ = ? (y ≠ 0)

Solution

Example

(3x⁴y)² = ? (x, y ≠ 0)

Solution

Zero Exponent

Formula

a⁰ = 1

Example

2⁰

Solution

Example

4x²y⁰⋅(-3xy)⁰ (x, y ≠ 0)

Solution

Negative Exponent

Formula

a^-m = 1a^m

Example

x^-4 (x ≠ 0)

Solution

Example

1x^-3 = ? (x ≠ 0)

Solution

Example

x^-5y⁷x²y^-1 = ? (x, y ≠ 0)

Solution