Properties of Exponents

Name that Property

100

a⁰=1

What is The Zero Exponent Property?

200

(ab)^m = (a^m)(b^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)(a^n) = a^(m+n)

What is the Product of Powers Property?

500

(a^m)^n = a^(mn)

What is the Power of a Power Property?

Negative and Zero Exponents

100

4⁰ = ?

1

200

-4,783,312,901⁰ = ?

-1

300

(x⁵y⁸)⁰

1

400

(x^3)^(-1)

1/(x^3)

500

a^-5

1/a⁵

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

(x^4)/(x^9)

1/(x^5)

Product of Powers and Power of a Product

100

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

a^7

200

(a²)(a²) = ?

a⁴

300

(a¹b³)⁴ = ?

(a⁴)(b¹²)

400

(x⁷y⁴)⁷

(x⁴⁹)(y²⁸)

500

(a^6)(b^4) = ?

(a^6)(b^4) - 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

(b^7)^7

b^49

400

(y^3)^11

y^33

500

(b^9)^10

b^90