Algebra 1 Section 8.1

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.

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

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

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

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

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

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

Example 5 Simplify (-2m4n)3( mn2)2. (-2)3(m4)3(n)3 • ( )2(m)2(n2)2 1 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

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

Homework: pp. 330-331