Exponential Rules

Product Rule

100

a^{5 .} a²

a⁷

200

x⁵ (x⁶)(x³)

x¹³

300

x² y⁶(xy^-2)

x³y⁴

400

x^{2 .} x^{0 .} x ^. x³

x⁶

500

x^1/2x^1/4y^3/9y^1/3

x^3/4 y^2/3

Power Rule

100

(x³)⁴

x¹²

200

[(-3)⁵)]²

(-3)¹⁰

300

(2a³⁾⁴

16a¹²

400

(-5xy⁴)²

25x²y⁸

500

(4a⁵b⁶c²)³

64a¹⁵b¹⁸c⁶

Quotient Rule

100

x⁴ / x³

x

200

18p⁸ / 6p⁴

3p⁴

300

-5x²y⁷z²/(15x^-4y³z²)

- x⁶y⁴/3

400

x⁶y^-4 / x⁶y²

1/y⁶

500

12x⁶ / 2x 

6x⁵

Power & Product

100

(m^{2 .} m³)⁴

m²⁰

200

(n ^. n²)³

n⁹

300

(5w³)²

25w⁶

400

(3ab²)⁴

81a⁴b⁸

500

(4q^{6 .} 7q²)³   (can use calculator)

21952q²⁴

Mixed Exponents

100

Simplify:  -3² 

-9

200

Simplify:  -5+ x⁰

-4

300

Simplify:

3x^{5 .} 4x

12x⁶

400

Simplify:  (-2)³

-16

500

(-8x²)⁵

-32768x¹⁰