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Lesson 7-4 Warm-Up ALGEBRA 1 “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. m n mn (a ) · a 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 ALGEBRA 1 More Multiplication Properties of Exponents LESSON 7-4 Additional Examples Simplify (a3)4. (a3)4 = a3 • 4 = a12 Multiply exponents when raising a power to a power. Simplify. ALGEBRA 1 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. = b–4 Simplify. 1 = b4 Write using only positive exponents. ALGEBRA 1 “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]. (ab)n = an · bn Example: (3x)4 = 34 x4 = 3 · 3 · 3 · 3 · x4 = 81x4 Example: ALGEBRA 1 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. ALGEBRA 1 More Multiplication Properties of Exponents LESSON 7-4 Additional Examples 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. ALGEBRA 1 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. = 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. ALGEBRA 1 More Multiplication Properties of Exponents LESSON 7-4 Lesson Quiz Simplify each expression. 1. (x4)5 3. (5a4)3 x20 125a12 5. (2w–2)4(3w2b–2)3 432 2 6 w b x(x5y–2)3 x16 y6 4. (1.5 105)2 2.25 1010 2. 6. (3 10–5)(4 104)2 4.8 104 ALGEBRA 1