Lesson 8.4 Multiplication Properties of Exponents Property: Raising a Power to a Power For every nonzero number a and integers m and n, (am)n = amn Examples: (54)2 = 54•2 58

Simplifying a Power Raised to a Power ALGEBRA 1 LESSON 8-4 Simplify (a3)4. Multiply exponents when raising a power to a power. (a3)4 = a3 • 4 Simplify. = a12 8-4

Simplifying an Expression With Powers ALGEBRA 1 LESSON 8-4 Simplify b2(b3)–2. b2(b3)–2 = b2 • b3 • (–2)  Multiply exponents in (b3)–2. = b2 • b–6 Simplify. = b2 + (–6) Add exponents when multiplying powers of the same base. Simplify. = b–4 1 b4 = Write using only positive exponents. 8-4

1. (c2)6(c6)4 **Remember to follow order of operations c12 • c24 c36 You Try 1. (c2)6(c6)4 **Remember to follow order of operations c12 • c24 c36 2. (d3)2d4 d6 • d4 d10

Raising a Product to a Power Property: Raising a Product to a Power For every nonzero number a and b and integer n, (ab)n = anbn. Example: (3x)4 = 34 x4 81x4

Simplifying a Product Raised to a Power ALGEBRA 1 LESSON 8-4 Simplify (4x3)2. (4x3)2 = 42(x3)2 Raise each factor to the second power. = 42x6 Multiply exponents of a power raised to a power. = 16x6 Simplify. 8-4

You Try (4g5) -2 4-2(g5) -2 4-2g-10 1 16g10

Simplifying a Product Raised to a Power ALGEBRA 1 LESSON 8-4 Simplify (4xy3)2(x3)–3. (4xy3)2(x3)–3 = 42x2(y3)2 • (x3)–3 Raise the three factors to the second power. = 42 • x2 • y6 • x–9 Multiply exponents of a power raised to a power. = 42 • x2 • x–9 • y6 Use the Commutative Property of Multiplication. = 42 • x–7 • y6 Add exponents of powers with the same base. 16y6 x7 = Simplify. 8-4

You Try: (2a3)5(3ab2)3 25(a3)5 •33a3(b2)3 25a15 • 33a3b6 32a15 • 27a3b6 864a18b6