ExponentsChelsie Wright

Exponents are a shorthand way to show how many times a number, called the base, is multiplied times itself.

Rule #1They must have the same base

To multiply powers of the same base, add the exponents! 

Example: a2a3 = a5

Solution 

The problem means:  Multiply the numbers, then combine the powers of x :

3x2· 4x5· 2x = 24x8

Two factors of x -- x2 -- times five factors of x -- x5 -- times one factor of x, produce a total of 2 + 5 + 1 = 8 factors of x :  x8.

Rule #2

Power of a product of factorsRaise each factor to that same power!

Example:(ab)3 = a3b3

Why do we do that?Again, according to what the symbols mean:(ab)3 = ab· ab· ab = aaabbb = a3b3.The order of the factors does not matter:

ab· ab· ab = aaabbb.

Rule #3Power of a power

To take a power of a power, multiply the exponents!

Example:(a2)3 = a2· 3 = a6

Why do we do that?Again, because of what the symbols mean:(a2)3 = a2a2a2 = a3· 2 = a6

Again, because of what the symbols mean:(a2)3 = a2a2a2 = a3· 2 = a6

Now you try some

Use Rule #1 to solve this problem

5x2· 6x4=

a)30x8 b)30x6

c)30x12 

Nope! The correct answer is 30x6

You multiply the base and add the exponents.

CORRECT!

Nope!The correct answer is 30x6

You multiply the base and add the exponents.

Use Rule #2 to solve the problem

(xy)4 =

a)xy4 b)x2 y4 c)x4 y4 

Nope!The correct answer is c)x4 y4 

Nope!The correct answer is c)x4 y4 

Correct!

Use Rule #3 to solve the problem

(x2)5 = a)x7

b)x10

c)x25

Nope!The correct answer is b)x10

Correct!

Nope! The correct answer is b)x10

Now that you know all three rules complete a

few more practice problems

(a4)8 =a)a12

b)a32

c)8a4

Nope!The correct answer is b)a32

Correct!

Nope!The correct answer is b)a32

(3x6)2 =a)9x12

b)6x12

c)9x36

Correct!

Nope!The correct answer is a)9x12

Nope!The correct answer is a)9x12

Works Cited"Decimals and Integers - Exponents - First Glance." Decimals and Integers - Exponents - First Glance. N.p., n.d. Web. 18 Feb. 2015."Three Rules of Exponents." Three Rules of Exponents. N.p., n.d. Web. 17 Feb. 2015.