Properties of Exponents

Multiplying Powers

100

m³(4m⁵)

4m⁸

200

(x+9)⁵(x+9)⁷

(x+9)¹²

300

(a³b)(ab⁴)

a⁴b⁵

400

(2x⁴)(3x⁰)(-x⁸)

-6x¹²

500

(2w³z⁷)(-8w⁴zm³)

-16w⁷z⁸m³

Dividing Powers

100

a¹⁰/a²

a⁸

200

18w¹⁴/9w¹⁴

2

300

m⁹n⁸/m⁰n⁴

m⁹n⁴

400

x¹⁰y³/yx⁵

x⁵y²

500

18p³d¹¹a⁴/3p³da²

6d¹⁰a²

Power to a Power

100

(a²⁵)³

a⁷⁵

200

(-3m⁴p⁶)³

-27m¹²p¹⁸

300

(a⁴/b³)⁵

a²⁰/b¹⁵

400

(5x⁷/2b⁵c²)²

25x¹⁴/4b¹⁰c⁴

500

(xy⁴)(2xy)³

8x⁴y⁷

Mix It Up

100

((9x^2)(-2x^3y))/(18xy)

-x^4

200

((-5x^5y^2)(7xy^⁵))/((25x)(7y^3))

(-x^5y^4)/(5

300

(-17y^7)/y

-17y^6

400

4^10/4^8

16

500

(9xyz)^2/(-21xy

(-27xyz^2)/(7)

Negative Exponents

100

x^-5/x^-10

x⁵

200

3m^7*x^3*m^-4*x^-8

3m^3x^-5

300

Simplify and write your answer with positive exponents. 

(w^-4h^-5)^3

1/(w^12h^15)

400

(24x^4y^6)/(-6x^11y^6)

Two possible answers:

-4x^-7

(-4)/x^7

500

(-2x^-6y^-5z^-4)^2*(3x^3y^2z^0)^2

Two possible answers:

36x^-6y^-6z^-8

or

36/(x^6y^6z^8)