Properties of Exponents – Part 1 Multiplication Learn multiplication properties of exponents.

The factors of a power, such as 74, can be grouped in different ways The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

MULTIPLYING POWERS WITH THE SAME BASE Words Numbers Algebra To multiply powers with the same base, keep the base and add the exponents. bm • bn = bm + n 35 • 38 = 35 + 8 = 313 MULTIPLYING POWERS WITH THE SAME BASE

Multiplying Powers with the Same Base Multiply. Write the product as one power. 1. 66 • 63 6 6 + 3 Add exponents. 6 9 2. n5 • n7 n 5 + 7 Add exponents. n 12

Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. 3. 25 • 2 2 5 + 1 Think: 2 = 2 1 2 6 Add exponents. 4. 244 • 244 24 4 + 4 Add exponents. 24 8

Power of Power Property Powers of powers with the same base: (am)n = amn multiply exponents (24)6 = 224 2(4•6)

Power of a Product Property Different bases, distribute power to each base and multiply. Examples: (a • b)4 = a4 • b4 = a4b4 (-3x)2 = (-3) 2• x 2 = 9x2

Practice! (32y3)2 (5a2b4)5 3(2•2) y(3•2) 34y6 81y6 55 a(2•5) b (4•5)

Practice! n3  n4 33 • 32 • 35 (-4xy3)3 8 • 88 n7 310 -64x3y9 89