Laws of Exponents

Products

100

x³ ⋅ x¹⁰

x¹³

200

2a³⋅5a²

10a⁵

300

m²n⁴⋅m³n

m⁵n⁵

400

3x²y³⋅4x⁵y²

12x⁷y⁵

500

−2a⁻³b⁴c²⋅5a⁶b⁻¹c³

-10a³b³c⁵

Quotients

100

x⁸ / x³

x⁵

200

12a⁷ / 3a⁴

4a³

300

m⁵n⁴ / mn³

m⁴n

400

18x⁶y⁸ / 6x²y³

3x⁴y⁵

500

-20a³b^-2c³ / 5a^-1b⁴c³

-4a⁴ / b⁶

Power of Power

100

(x²)⁷

x¹⁴

200

(3a⁴)²

3²a⁸ or 9a⁸

300

(m³n²)⁴

m¹²n⁸

400

(2x^-2y³)³

2³y⁶ / x⁶ or 8y⁶ / x⁶

500

(-3a^-2b³c^-1)^-2

a⁴c² / 3²b⁶

Zero/Negative

100

f⁰

1

200

12(w⁰)

12

300

a^-44

1 / a⁴⁴

400

x^-3y² / z^-2

y²z² / x³

500

6a^-2b⁰c³ / 3a⁴b^-1c^-2

2b¹c⁵/a⁶

Power of a Quotient

100

(x³ / b⁵)⁴

x¹² / b²⁰

200

(t³w⁵ / tw)²

t⁵w⁸

300

(2m²n)² / 4m³

mn²

400

(5x³y^-2 / z⁴)³

5³x⁹/y⁶z¹²

500

(2h^-1r⁶p⁷ / h³r³p²)³

2³r⁹p¹⁵ / h^-12