Multiplication of Exponents Notes

What is an Exponent? An exponent means that you multiply the base by

itself that many times.

For example

xx4 4 = = x x ● ● xx ●● xx ●● xx

226 6 = = 2 2 ● ● 22 ● ● 22 ● ● 22 ● ● 22 ● ● 22 = 64= 64

Power – a number produced by raising a base to an exponent. (the term 27 is called a power.)

Exponential form – a number written with a base and an exponent. (23)

Exponent – the number that indicates how many times the base is used as a factor. (27)

Base – when a number is being raised to a power, the number being used as a factor. (27)

Vocabulary

Parts of a Power

power

24 exponen

tbase

Say: “2 to the fourth power”

The Invisible ExponentWhen an expression does not have a visible exponent its

exponent is understood to be 1.

Zero ExponentWhen anything, except 0, is raised to the zero power

it is 1.

For example

( if a ≠ 0)

( if x ≠ 0)

Multiplication RuleWhen multiplying two expressions with the same base you add their exponents.

For example

Example 1

(222) (22222)

Example 2

Written in multiplication form:

Using Rule:

Example 3

Example 4

Remember:

Example 5

Multiply coefficients and add exponents of like bases

(-2x3y5)(3xy3)(x2y)

-6x6y9

-6x(3+1+2)y(5+3+1)

Example 6

In order to simplify you must distribute first.

Since you are multiplying when you distribute you must use the multiplication rule for exponents.

You Try Simplify each expression

1.

2.

3,

4.

5.

6.

You Try: Simplify(remember when adding only add

coefficients of like terms)

1.

2.

3.

4.