Properties of Exponents

Product of Powers Property

100

(x^y)(x^z)=?

x^y+z

200

(x²)(x⁴)=?

x⁶

300

(x¹²)(x¹¹)=?

x²³

400

(x²¹³)(x¹²⁷)=?

x³⁴⁰

500

(x^1/2)(x¹²⁰⁰)(x²³)

x^1223.5

Power of a Power Product

100

(a^x)^y=?

a^xy

200

what is x⁰?

1

300

(x⁷)¹⁰=?

x⁷⁰

400

(x¹⁴)¹¹=?

x¹⁵⁴

500

(x^1/2)⁴⁴=?

x²²

Power of a Product Property

100

(ab)^x=?

a^xb^x

200

(5x)²=?

25x²

300

(12ab)³=?

1728a³b³

400

(15a²b³)⁴=?

50,625a⁸b¹²

500

(17a⁵b^1/2)²

289a¹⁰b

Quotient of Powers Property

100

a^x/a^y=?

a^x-y

200

x⁶/x³=?

x³

300

6x⁴/9x³=?

2x/3

400

7x⁸/14x⁵=?

1x³/2

500

a^-x=?

1/a^x 

Power of a Quotient Property

100

(a/b)^x=?

a^x/b^x

200

(x/3)²=?

x²/9

300

(x/5)¹⁰=?

x¹⁰/9,765,625

400

(x/15)⁸=?

x⁸/2,562,890,625

500

(5b²/15b^-5)⁰=?

1