Properties of Exponents

Negative Exponent

100

x^-1 = ?

x^-1 = 1/x

200

x^-2 = ?

x^-2 = 1/x²

300

-(2x)⁰ = ?

-1

400

3x^-2 = ?

 3/x²

500

x^-x = ?

x^-x = 1/x^x

Product Property

100

x⁴ * x⁶ = ?

x⁴ * x⁶ = x¹⁰

200

x^-2 * x⁸ = ?

x^-2 * x⁸ = x⁶

300

2x³ * 3x² = ?

2x³ * 3x² = 6x⁵

400

2x⁴ * 2x⁴ * 2x⁴ = ?

2x⁴ * 2x⁴ * 2x⁴ = 8x¹²

500

5x⁷y^-3 * 6x^-5y^-5 = ?

5x⁷y^-3 * 6x^-5y^-5 = 30x²y^-8 = 30x²/y⁸

Quotient Property

100

 x^8/x^7

x

200

Simplify:  

x^10/x^8

x^2

300

4x⁰/2x⁷ = ?

4x⁰/2x⁷ = 2/x⁷

400

(xy)⁴/xy⁸ = ?

(xy)⁴/xy⁸ = x³y^-4 = x³/y⁴

500

5x^-10y^-7/8x^-5y³ = ?

5x^-10y^-7/8x^-5y³ = 5x^-5y^-10 = 5/(x⁵y¹⁰)

Power of Powers

100

(x²)⁴ = ?

(x²)⁴ = x⁸

200

(x^-3)^-2 = ?

(x^-3)^-2 = x⁶

300

((x⁴)^-2)^-1 = ?

((x⁴)^-2)^-1 = x⁸

400

(8x³)² = ?

(8x³)² = 64x⁶

500

(5x³y^-2)⁴ = ?

(5x³y^-2)⁴ = 625x¹²y^-8 = (625x¹²)/y⁸

Mixed Bag

100

(x^-9 * x^-3)² = ?

(x^-9 * x^-3)² = 1/x²⁴

200

(x^-7/x^-3) * (x⁴/x^-5) = ?

(x^-7/x^-3) * (x⁴/x^-5) = x⁵

300

((x^-5)³) / (x^-9 * x⁸) = ?

((x^-5)³) / (x^-9 * x⁸) = x^-14 = 1/x¹⁴

400

(x²y)² * (xy²)² = ?

(x²y)² * (xy²)² = x⁶y⁶

500

(4x³y^-1 * 2x^-3y) / (2x²) = ?

(4x³y^-1 * 2x^-3y) / (2x²) = 4x^-2 = 4/x²