Properties of Exponents

Negative Exponent

100

x^-1 = ?

1/x

200

x^-2 = ?

 

1/x^2

300

x⁰ = ?

x⁰ = 1

400

x^-1/2 = ?

1/(x^(1/2

500

x^-n = ?

1/x^n

Product Property

100

x⁴ * x⁶ = ?

 x¹⁰

200

x^-2 * x⁸ = ?

 x⁶

300

2x³ * 3x² = ?

6x⁵

400

2x⁴ * 2x⁴ * 2x⁴ = ?

 8x¹²

500

5x⁷y^-3 * 6x^-5y^-5 = ?

(30x^2)/y^8

Quotient Property

100

x⁸/x⁷ = ?

x

200

x^-10/x^-8 = ?

1/x^2

300

4x⁰/2x⁷ = ?

4x⁰/2x⁷ = 2/x⁷

400

(x-y)⁴/(x-y)⁸ = ? Be creative (x-y) is ONE base.

(x-y)^-4

500

5x^-10y^-7/8x^-5y³ = ? 

No Negative Exponents in your Answer

5/ (x^5y^10

 

5x^-5y^-10

Power of Powers

100

(x²)⁴ = ?

 x⁸

200

(x^-3)^-2 = ?

 x⁶

300

((x⁴)^-2)^-1 = ?

 x⁸

400

(8x³)² = ?

64x⁶

500

(5x³y^-2)⁴ = ?

625x¹²y^-8

Mixed Bag

100

(x^-9 * x^-3)² = ?

1/x^24

200

(x^-7/x^-3)* (x^4/x^-5)=

x⁵

300

(x^-5)^3/(x^-9 * x^8)

 x^-14 or 

1/x^14

400

(x²y)² * (xy²)² = ?

 x⁶y⁶

500

(4x³y^-1 * 2x^-3y) / (2x²) = ?

4x^-2