Properties of Exponents

Name that Property

100

a⁰=1

What is The Zero Exponent Property?

200

(ab)^m = a^mb^m

What is The Power of a Product Property?

300

(a/b)^m = a^m/b^m

What is the Power of a Quotient Property?

400

(a^m)(aⁿ) = a^m+n

What is the Product of Powers Property?

500

(a^m)ⁿ = a^(mn)

What is the Power of a Power Property?

Quotient of Powers and Power of a Quotient

100

(a^m)/(a^n) = ?

a^(m-n)

200

(y⁶)/(y³)

y³

300

x¹⁰/x³ = ?

x⁷

400

x²⁴/x²³ = ?

x

500

x⁴/x⁹

x^(-5) OR 1/(x⁵)

Product of Powers and Power of a Product

100

(a^2)(a^5) = ?

a^7

200

(a²)(a²) = ?

a⁴

300

(x⁷y⁴)⁷

x⁴⁹y²⁸

400

(ab³)⁴ = ?

a⁴b¹²

500

(a⁶)(b⁴) = ?

(a⁶)(b⁴) - this cannot be simplified because a and b are different.

Power of a Power

100

(a^m)ⁿ = ?

a^mn

200

(x³)⁶

x¹⁸

300

(b⁷)⁷

b⁴⁹

400

(y³)¹¹

y³³

500

(b⁹)¹⁰

b⁹⁰

Miscellaneous

300

Name that property

x⁷/x³ = x^7-3 = x⁴

What is the Quotient of a Powers Property

400

(a⁷)(a^-3)

a⁴

500

(xy²/z)³

x³y⁶/z³