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^maⁿ = 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

g^-5 = ?

1/g⁵

300

(2x⁵y⁸)⁰

1

400

h^-3j⁵k^-2

j⁵/h³k²

500

(15a⁴b²)/(25a⁶b^-5)

(3b⁷)/(5a²)

Quotient of Powers and Power of a Quotient

100

(a^m)/(aⁿ) = ?

a^(m-n)

200

(y⁶)/(y²)

y⁴

300

(x⁷/y³)² = ?

x¹⁴/y⁶

400

(2d¹⁰e²)/(6d⁵e²)

(d⁵)/3

500

(x⁴)/(x⁹)

x^-5 OR 1/x⁵

Product of Powers and Power of a Product

100

(a²)(a⁵) = ?

a⁷

200

a⁶b⁴ = ?

a⁶b⁴ - this cannot be simplified because a and b are different.

300

(ab³)⁴ = ?

a⁴b¹²

400

(4y⁷)(5y⁴)

20y¹¹

500

5a⁸ * -7a⁶ = ?

-35a¹⁴

Power of a Power

100

(a^m)ⁿ = ?

a^mn

200

(x³)⁶

x¹⁸

300

(2b⁷)⁷

128b⁴⁹

400

((3x⁴)(y¹¹))³

(27x¹²)(y³³)

500

((a⁴)/(b⁹))^-5

(b⁴⁵)/(a²⁰)