algebra 1 lesson 7-4 warm-up. algebra 1 “more multiplication properties of exponents” (7-4) what...
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ALGEBRA 1
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.
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
ALGEBRA 1
Simplify (a3)4.
Multiply exponents when raising a power to a power.(a3)4 = a3 • 4
Simplify.= a12
More Multiplication Properties of ExponentsLESSON 7-4
Additional Examples
ALGEBRA 1
Simplify b2(b3)–2.
b2(b3)–2 = b2 • b3 • (–2) Multiply exponents in (b3)–2.
= b2 + (–6) Add exponents when multiplying powers of the same base.
Simplify. = b–4
= b2 • b–6 Simplify.
1 b4= Write using only positive exponents.
More Multiplication Properties of Exponents
LESSON 7-4
Additional Examples
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 ].
Example: (3x)4 = 34 x4 = 3 · 3 · 3 · 3 · x4 = 81x4
Example:
(ab)n = an · bn
ALGEBRA 1
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.
More Multiplication Properties of ExponentsLESSON 7-4
Additional Examples
ALGEBRA 1
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.
More Multiplication Properties of ExponentsLESSON 7-4
Additional Examples
16y6
x7= Simplify.
= • • Change negative exponents into positive exponents.
161
1x7
y6
1
ALGEBRA 1
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)2Raise 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 joulesSimplify.Write in scientific notation and add label.
More Multiplication Properties of ExponentsLESSON 7-4
Additional Examples
ALGEBRA 1
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
x20x16
y6
125a122.25 1010
432w2b6
4.8 104
More Multiplication Properties of ExponentsLESSON 7-4
Lesson Quiz