1. 5.1
Integer Exponents and Scientific Notation

2. Using the Product Rule for Exponents
Example 1
Apply the product rule for exponents, if possible, in each case.
(a) (b)
(c) (d)
Answer
(a)
(b)
(c)
(d)

3. Example 2
Using 0 as an Exponent
Evaluate.
(a) (b)
(c) (d)
Answer
(a)
(b)
(c)
(d)

4. Using Negative Exponents
Example 3
Using Negative Exponents
Write with only positive exponents.
(a) (b)
(c) (d) Evaluate
Answer
(a)
(b)
(c)
(d)

5. Using Negative Exponents
Example 4
Using Negative Exponents
Evaluate.
(a) (b)
Answer
(a)
(b)

6. Using the Quotient Rule for Exponents
Example 5
Apply the quotient rule, if possible, and write each result with only positive exponents.
(a) (b) (c)
Answer
(a)
(b)
(c) The quotient rule does not apply.

7. Using the Power Rules for Exponents
Example 6
Using the Power Rules for Exponents
Simplify, using the power rules.
(a) (b) (c)
Answer
(a)
(b)
(c)

8. Using Negative Exponents with Fractions
Example 7
Write with only positive exponents and evaluate.
Answer

9. Using the Definitions and Rules for Exponents
Example 8
Simplify. Assume that all variables represent nonzero real numbers.
(a) (b)
(c) (d)
Answer
(a)

10. Using the Definitions and Rules for Exponents (continued)
Example 8
(b)
(c)
(d)

11. Writing Numbers in Scientific Notation
Example 9
Write each number in scientific notation.
(a) 29,800,000 (b)
Answer
(a) 29,800,000 = 2.98 × 107
(b) = 5.03 × 10–8

12. Converting from Scientific Notation to Standard Notation
Example 10
Write each number in standard notation.
(a) 2.51 × 103 (b) –6.8 × 10–4
Answer
(a) 2.51 × 103 = 2510
(b) –6.8 × 10–4 = –

13. Using Scientific Notation in Computation
Example 11
Evaluate
Answer

14. Using Scientific Notation to Solve Problems
Example 12
The distance to the Sun is 9.3 × 107 miles. How long would it take a rocket traveling at 3.2 × 103 miles per hour to reach the Sun?
Answer
d = rt, so
It will take about 2.9 × 104 or 29,000 hours to reach the sun.