Name _________________________________________________________
RETEACHING
Date ____________________________
3-8
LAWS OF EXPONENTS
You can use the rules of exponents in simplifying expressions
containing numbers in exponential form.
Product Rule: To multiply numbers with the same base, add the exponents:
am • an am+n
Quotient Rule: To divide numbers with the same base, subtract the exponents:
am an am-n
Power Rule: To raise an exponential number to a power, multiply the exponents:
(am)n am • n
E x a m p l e 1
Simplify.
a. 33 • 32
Solution
a. 33 • 32 33 2 35
33 • 32 (3 • 3 • 3) • (3 • 3) 35
E x a m p l e
Simplify (42)3.
b. 54 52
b. 54 52 54 2 52
•5 • 5
5 • 5
54 52 52
5•5
2
Solution
(42)3 42 • 3 46
(42)3 42 • 42 • 42 (4 • 4) • (4 • 4) • (4 • 4) 46
EXERCISES
Use the product rule to simplify.
1. 26 • 28
2. 53 • 56
3. 104 • 107
4. 45 • 4
Use the quotient rule to simplify.
5. 78 7
6. 23 22
7. 46 46
8. 109 106
Use the power rule to simplify.
9. (23)4
10. (52)0
11. (72)10
13. Which of the following are equal
to 210?
b. (22)5
c. 210 20
a. 22 • 25
© Glencoe/McGraw-Hill
12. (103)6
14. Which of the following are equal to
twice 216?
b. 217
c. 131,072
d. 232
a. 416
25
MathMatters 1