Exponent Laws

Multiplying Powers

100

(x⁵)(x⁴)

x⁹

200

(b²)(b⁵)(b³)

b¹⁰

300

(4x³)(2x³)

8x⁶

400

(4x³)(2x³)(y³)(y²)

8x⁶y⁵

500

(2x²y³)(-3x³y⁴)(2)

-12x⁵y⁷

Dividing Powers

100

x¹² ÷ x³

x⁹

200

(-5)¹⁰  ÷ (-5)²

-5⁸

300

24x²¹ ÷ 8x³

3x¹⁸

400

x²²y¹⁷ ÷ x⁶y⁴

x¹⁶y¹³

500

(2⁶)x⁸y⁵ ÷ (2²)x⁴y⁴

(2⁴)(x⁴)(y)

Power to a Power

100

(x²)³

x⁶

200

(2³)⁴

2¹²

^{= 4096}

300

(x⁴)³  x  (x³y)³  

x²¹y³

400

(2x³)² × (3x²)²

(2²)(x⁶) × (3²)(x⁴) 

= (2²)(3²)(x¹⁰)    [also = (4)(9)(x⁴) = 36x¹⁰]

500

(5²x³)²  x  (xy²)⁴

5⁴x¹⁰y⁸

Simplifying Variable expressions

100

((x⁵)(x³)) ÷ x¹

x⁷

200

((x⁵)(x²)) ÷ (x⁶)

x¹       or     x  

300

16x⁵ ÷ (2x²)²

4x

400

[(3x²y³)(2xy²)] ÷ 2xy²

3x²y³

500

(10x⁶y¹¹) (x⁴y³)÷ 2x³y⁵

5x⁷y⁹