Properties of Exponents

Vocabulary

100

the number that gets multiplied by itself when using an exponent.

base

200

the method of expressing numbers in terms of powers (how many times a number multiplied by itself).

exponent

300

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

What is The Power of a Product 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

100

(a^m/(aⁿ) = ?

a(^m-n)

200

(y⁶)/(y³)

y³

300

(x¹⁰)/(x^-3) = ?

x¹³

400

(10x²⁴)/(2x²³) = ?

5x

500

(8x^-4)/(4x⁹)

2x^-13

Product of Powers

100

(a²)(a⁵) = ?

a⁷

200

(a²)(a^-2) = ?

a^-4

300

(2 x 2³)⁴= ?

2¹⁶

400

(2a⁷ x 3a⁴)⁵

7,776a⁵⁵

500

(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

b^-49

400

(2y¹¹)³

8y³³

500

(-6b⁹c⁴)⁸

36b¹⁸c⁸