Multiplication Property ofExponents

8-1

What do the following mean?

1) X3

2) Y5

3) 24x2x3

• X · X · X

• Y · Y · Y · Y · Y

• 2 · 2 · 2 · 2 · (X · X) · (X · X · X)• 16X5

Vocabulary

• X3

– X is the base– 3 is the exponent

• tells us how many times to multiply the base by itself

Product of Powers Rule

• When you multiply powers that have the same base, you add the exponents.

• Ex:• y3y5 = y3+5 = y8

1) x6x11 =

2) 2322 = x17

25

Complete the equation…

1) (5?)2 = 510

2) (x5)? = x15

3) [-2)8]2 = (-2)?

1) 5

2) 3

3) 16

Power to Power Rule

• When you raise an exponent to a power, you multiply the exponents

• Ex: (x3)4 = x12

Power of a Product ( ) Rule

• When you raise a set of ( ) to a power, you have to raise everything in the ( ) to the power.

Ex: (a • b)3 = a3 • b3

(3x2)4 = 34 • (x2)4 = 34 • x8 = 81x8

Simplify

1) (2mn)6

2) (-rst)5

3) -4x • (x3)2

4) (5y2)3 • (y3)2

1) 64m6n6

2) -r5 s5 t5

3) -4x7

4) 125x12

Homework

• Pg. 446#20-60 (e), 70-73 all