Transcript Zero and Negative Exponents

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