1. Algebra 1
Section 8.1

2. Properties of Exponents
Product Property: xa • xb = xa+b
To multiply powers with like bases, add the exponents.
Power Property: (xa)b = xab
To raise a power to a power, multiply the exponents.

3. Example 1 Add the exponents. x5 • x2 = x5+2 = x7
(b) Multiply the exponents.
(x5)2 = x5(2) = x10

4. Example 1
Remember the order of operations: Raising to powers comes before multiplication.
y4(y3)2
y4(y6)
y10

5. Example 2
You can apply the Commutative and Associative Properties of Multiplication.
3x2 • 5x = (3 • 5)(x2+1)
= 15x3
Remember that x = x1 !

6. Example 3 Simplify -8x2yz3(xyz2). -8(x2 • x)(y • y)(z3 • z2)

7. Example 4 Simplify (-ab2)3. (-ab2)(-ab2)(-ab2) -1(-1)(-1)(aaa)(b2b2b2)

8. Properties of Exponents
The Commutative and Associative Properties can be used to show that the power of a product is equal to the product of the powers.
(abc)n = anbncn

9. Example 5 Simplify (-2m4n)3( mn2)2. (-2)3(m4)3(n)3 • ( )2(m)2(n2)21 6
(-2)3(m4)3(n)3 • ( )2(m)2(n2)2 1 6
-8m12n3 ( )m2n4 1 36
-8( )m12+2n3+4 1 36
= - m14n7 2 9

10. Example 6 Simplify x2xy2 + 3xyx2 – 5x3y2. First, simplify each term:
x3y2 + 3x3y – 5x3y2
Then, combine like terms:
-4x3y2 + 3x3y

11. Homework: pp