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Lessons # 8.3-8.4: Zero and Negative Exponents;
Scientific Notation
Objectives:
 Use zero and negative exponents.
 Read and write numbers in scientific notation.
Homework Assignment: Study # 8.3-8.4; Review notes/examples;
Handouts for # 8.3-8.4
8.3 Define and Use Zero and Negative Exponents
DEFINITION OF ZERO AND NEGATIVE EXPONENTS
Words
a to the zero
power a0 is 1.
a–n is the
reciprocal of an.
an is the reciprocal
of a–n.
Algebra
a0 = ____, a ≠ 0
Example
50 = ____
a–n = ____ ,a ≠ 0
2–1 = ____
an = ____ ,a ≠ 0
2 = ____
Example 1
a. 2–3 =
1 3
4 

c.   =
b. (-10)° =
d.
0–7 =
2
PROPERTIES OF EXPONENTS
Let a and b be real numbers, and let m and n be integers.
am. an = a ______
____________________ property
(am)n = a ____
____________________ property
(ab)m = _______
____________________ property
am
= a _____ , a ≠ 0
an
m
a 
  = ____ b ≠ 0
b 
____________________ property
____________________ property
b
Example 2
a. (-5)4 • (-5)– 4 =
b. (5-2)–2 =
c. 1 =
42
2
d. 3 =
31
Checkpoint.
1.
1  1
 
8 
b
6 1
3. 6
1
2. 32
4. (5–1)2
3
Example 3
Simplify the expression. Write your answer using only positive
exponents.
a)
Checkpoint.
4
5. 6 fg
2f2g
6. (3yz2)–2
8.5. SCIENTIFIC NOTATION
A number is written in scientific notation when it is of the
form___________ where 1 ≤ c < 10 and n is an integer.
Number
Standard form Scientific notation
Sixteen million ____________ _______________
Two
____________ _______________
hundredths
Example 4
Write numbers in scientific notation
a. 7,820,000 =
b. 0.00401 =
Example 5
Write numbers in standard form
a. 3.89 × 109 =
b. 9.097 × 10–5 =
4
Checkpoint.
7. a) Write the number 0.0899 in scientific notation:
b) Write the number 6.0001 x 107 in standard form:
Example 6
Order 3.2 × 10–4, 0.0004, and 2.8 x 10–5 from least to greatest:
Example 7
Evaluate the expression. Write your answer in scientific notation.
a. (5.6 x 10–4)(1.4 x 10–5) =
b. (3.2 x 102)3 =
c.
3.5 × 10 –3
1.75 × 10 –5
Checkpoint. Simplify the expression.
8. (2.01×10–7)2 =
9.
4.8 × 10–4
6 × 10–4