Exponent Rules

Product Rule

1

x⁴ • x ⁵

x ⁹

2

2x ³ • 3x ²

6x ⁵

3

(5b ³)(-2b)

-10b ⁴

4

(6xy ² )(xy)

6x ²y³

5

(-4a²)(4a²b) 

-16a⁴b

Quotient Rule

1

2x² / x

2x

2

4x³ / 2x

2x²

3

-6x/2x²

-3/x

4

36xy² / 6x²y

6y/x

5

25x³y⁴/ 35x³y

5y³/7

Power of a Power

1

(y ⁶ )⁷

y ⁴²

2

(x ⁶ y²)³

x ¹⁸ y ¹⁸

3

(3x³)⁴

81x¹²

4

(2x³y³)^-2

1/(4x⁶y⁶)

5

(4x⁴y^-4)³

64x¹²/ y ¹²

Negative Exponent

1

x ^-6

1/x ⁶

2

7^-2

1/49

3

x ⁹ • x ^-7

x²

4

x ^-4 / x ^-9

x ⁵

5

24x⁶ / 12x^-8

2x ¹⁴

Mixed Bag

1

x ^-1 / x ^-8

x ⁷

2

52x⁶ / 13x^-7

4x¹³

3

(5x²y)(2x⁴y^-3)

10x⁶ / y ²

4

(3x²y^-3)/(12x⁶y³)

1/(4x⁴y⁶)

5

[(2a³b²c⁰)/(3a²b³c⁷)]^-2

9b²c¹⁴ / 4a²