Properties of Exponents

Name that Property

100

(a^m)(aⁿ) = a(^{m + n})

What is the Product of Powers 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

3 (radical 5²) = 5^2/3

Radical Exponent Property

500

(a^m)ⁿ = a^mn

What is the Power of Powers Property?

Quotient of Powers

100

(a^m)/(aⁿ) = ?

a^m-n

200

(y⁶)/(y³)

y³

300

(x¹⁰)/(x³) = ?

x⁷

400

(x²⁴)/(x²³) = ?

x

500

(x⁴)/(x⁹)

x^-5 

Product of Powers

100

(a²)(a⁵) = ?

a⁷

200

(a²)(a²) = ?

a⁴

300

[(a¹)(b³)]⁴ = ?

(a⁴)(b¹²)

400

[(x⁷)(y⁴)]⁷

(x⁴⁹)(y²⁸)

500

(a⁶)(b⁴) = ?

(a⁶)(b⁴) - this cannot be simplified because the bases are different.

Power of Powers

100

(a^m)ⁿ = ?

a^mn

200

(x³)⁶

x¹⁸

300

(b⁷)⁷

b⁴⁹

400

(y³)¹¹

y³³

500

(b⁹)¹⁰

b⁹⁰

Solve for x

100

(4^x/2)(4^x/5) = 4⁸

x = 80/7

200

(10^x/6)(10^x/8) = 10¹⁰

x = 240/7

300

16^{(x - 3)} = 2^{(x - 6)}

x = 2

400

64^{(x + 1)} = 4^x+7

x = 2