Lesson 7-4 Warm-Up

“More Multiplication Properties of Exponents” (7-4) What happens when you raise a power to a power? Rule: When you raise a power to a power [Example: (am)n ], multiply the powers together. Example: (72)3 = (72) · (72) · (72) = (7 · 7) · (7 · 7) · (7 · 7) = 76 Example: (a6)2 = a6 · a6 = (a · a · a · a · a · a) · (a · a · a · a · a · a) = a12 (am)n · amn

Multiply exponents when raising a power to a power. (a3)4 = a3 • 4 More Multiplication Properties of Exponents LESSON 7-4 Additional Examples Simplify (a3)4. Multiply exponents when raising a power to a power. (a3)4 = a3 • 4 Simplify. = a12

Multiply exponents in (b3)–2. More Multiplication Properties of Exponents LESSON 7-4 Additional Examples 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.

“More Multiplication Properties of Exponents” (7-4) What happens when you raise a product (for example, a variable and a coefficient, like 4x) to a power? Rule: When you raise a product to a power [Example: (ab)m, where a and b are nonzero numbers), raise each multiplicand (a and b) to the power separately]. Example: (3x)4 = 34  x4 = 3 · 3 · 3 · 3 · x4 = 81x4 Example: (ab)n = an · bn

Raise each factor to the second power. More Multiplication Properties of Exponents LESSON 7-4 Additional Examples 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.

(4xy3)2(x3)–3 = 42 • x2 • (y3)2 • (x3)–3 More Multiplication Properties of Exponents LESSON 7-4 Additional Examples Simplify (4xy3)2(x3)–3. (4xy3)2(x3)–3 = 42 • x2 • (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. 16 1 = • • Change negative exponents into positive exponents. 1 x7 y6 1 16y6 x7 = Simplify.

Raise each factor within parentheses to the second power. More Multiplication Properties of Exponents LESSON 7-4 Additional Examples An object has a mass of 102 kg. The expression 102 • (3  108)2 describes the amount of resting energy in joules the object contains. Simplify the expression. 102 • (3  108)2 = 102 • 32 • (108)2 Raise each factor within parentheses to the second power. = 102 • 32 • 1016 Simplify (108)2 = 10(8 • 2) . = 32 • 102 • 1016 Use the Commutative Property of Multiplication. = 32 • 102 + 16 Add exponents of powers with the same base. = 9  1018 joules Simplify. Write in scientific notation and add label.

Simplify each expression. 1. (x4)5 2. x(x5y–2)3 More Multiplication Properties of Exponents LESSON 7-4 Lesson Quiz Simplify each expression. 1. (x4)5 2. x(x5y–2)3 3. (5a4)3 4. (1.5  105)2 5. (2w–2)4(3w2b–2)3 6. (3  10–5)(4  104)2 x16 y6 x20 125a12 2.25  1010 432 w2b6 4.8  104