1. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
(For help, go to Lessons 1-2 and 1-6.)
Simplify each expression. 1 42
 22
4. (–3)3 5. –  12
Evaluate each expression for a = 2, b = –1, c = 0.5. a 2a bc c ab bc
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2. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
1. 23 = 2 • 2 • 2 = 8
= =
3. 42  22 = = = = 4
4. (–3)3 = (–3)(–3)(–3) = 9(–3) = –27
5. –33 = –(3 • 3 • 3) = –(9 • 3) = –27
6. 62  12 = 36  12 = 3
for a = 2: =
for b = –1, c = 0.5: = –1
for a = 2, b = –1, c = 0.5: = = 4
Solutions 1 42 1
4 • 4 1 16 42 22
4 • 4
2 • 2 16 4 a 2a 2
2 • 2 1 2 bc c
–1 • 0.5
0.5 ab bc
2 • (–1)
(–1) • 0.5 2
0.5
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3. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
Simplify. =
Use the definition of negative exponent. 1 32 a.
3–2
Simplify. 1 9 = b.
(–22.4)0
Use the definition of zero as an exponent.
= 1
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4. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
Simplify 1
x –3 a.
3ab –2 1 b2
Use the definition of negative exponent.
= 3a b.
Rewrite using a division symbol.
= 1  x –3
= 1  1
x 3
Use the definition of negative exponent.
Simplify. 3a
b 2 =
= 1 • x 3
Multiply by the reciprocal of , which is x 3. 1 x3
= x 3
Identity Property of Multiplication
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5. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
Evaluate 4x 2y –3 for x = 3 and y = –2.
Method 1: Write with positive exponents first.
4x 2y –3 =
Use the definition of negative exponent.
4x 2
y 3
Substitute 3 for x and –2 for y.
4(3)2
(–2)3 = 36 –8 –4 1 2 =
Simplify.
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6. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
(continued)
Method 2: Substitute first.
4x 2y –3 = 4(3)2(–2)–3
Substitute 3 for x and –2 for y.
4(3)2
(–2)3 =
Use the definition of negative exponent. 36 –8 –4 1 2 =
Simplify.
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7. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
In the lab, the population of a certain bacteria doubles every month. The expression 3000 • 2m models a population of 3000 bacteria after m months of growth. Evaluate the expression for m = 0 and m = –2. Describe what the value of the expression represents in each situation.
a. Evaluate the expression for m = 0.
3000 • 2m = 3000 • 20   Substitute 0 for m.
= 3000 • 1 Simplify.
= 3000
When m = 0, the value of the expression is This represents the initial population of the bacteria. This makes sense because when m = 0, no time has passed.
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8. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
(continued)
b. Evaluate the expression for m = –2.
3000 • 2m = 3000 • 2–2 Substitute –2 for m.
= 3000 • Simplify.
= 750 1 4
When m = –2, the value of the expression is 750. This represents the 750 bacteria in the population 2 months before the present population of 3000 bacteria.
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9. Zero and Negative Exponents
ALGEBRA 1 LESSON 1-7
Simplify each expression.
1. 3–4 2. (–6)0
3. –2a0b–2 4.
• • 3–2
1 81 1 2 b2 – k
m–3
km3
8000
500
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