EXPONENT RULES & PRACTICE
1. PRODUCT RULE: To multiply when two bases are the same, write the base and ADD the exponents.
· Examples:
A. · B. 2 · 2 2
C. 2. QUOTIENT RULE: To divide when two bases are the same, write the base and SUBTRACT the exponents.
Examples:
A.
B.
3
C.
3. ZERO EXPONENT RULE: Any base (except 0) raised to the zero power is equal to one.
Examples:
A. 1
B. 6 1
C. 7
1
!
4. POWER RULE: To raise a power to another power, write the base and MULTIPLY the exponents.
·
Examples:
A. C. " "
B. 3 3
5. EXPANDED POWER RULE:
# #
$# % # Examples:
A. 2 2
8
C. $ % B. 6 6 36 )
' (
)
*
)
D. $ % + ,
6. NEGATIVE EXPONENTS: If a factor in the numerator or denominator is moved across the fraction bar, the sign
of the exponent is changed.
-
$# %
# $ %
Examples:
A. D. $ %
F.
0 - 1
2 -) 3 -4
B. 4 $ % ,
1 2 ) 3
0
C. /4 E. 3 /2 /6 G. /2 $
%
)
)
%
$
*
)
CAUTION: / 5 For example: /3 5 REMEMBER: An exponent applies to only the factor it is directly next to unless parentheses enclose other factors.
Examples:
B. /3 /9
A. /3 /3/3 9
EXPONENTS PRACTICE
Simplify:
1. 3 · 4
15.
2. 4 · 2
3. · 4. 2 · 2
5.
6.
7
28.
)
17. $
)
%
%
9. 20. 7
)
13. 289 89
14. 2:; :;
,
-7
-)
->
,
31.
32.
34.
-)
23. · 7
-*
-*
-
,
33. 2 21. -
22.
10. -4
29. : : : 30.
19. +
8. /9
12.
27.
18. $
)
7. 8
11.
16.
,
) -)
7
35. 4 24. 36. 5 2 25. < · +
37. $ 0 1)2 %
26. = = = +0 1 2 @
0 1 2 @
38. $ 0 12 7 %
EXPONENTS PRACTICE ANSWERS
16. 1. 192
2. 8 17.
3. 4. 4
18.
20.
7. 1
*
31. 2
4,
32.
33.
<
34.
22. 16
9. 35.
23. 10. 36.
24. ,
11. 3 12. 2 14. 16: ;
15. 30. 21. 8. /1
13. 48 + 9
>
19. 7
5. 36
6.
29. B)
4
25. 37.
26. A
38.
27. +
28. 4
),
,
,
7
4
4
,
0) 1 ) 2 4
<1 2 4)
0