Laws of Exponents
Name:__________________________________ Period:__________
HW: 13.1A
Vocabulary
power
Exponent
base
1. The _________________ of a power is the number of times that the factor is repeatedly
multiplied
2. An expression used to represent a factor as repeated multiplication is called a ___________.
3. The ______________________ of a power is the repeated factor in a power.
Problem Set
State the base and the exponent of each power. Then evaluate to find the value of the power.
4.
94
5. 182
Base:_______ Exponent:_________
Base:_______ Exponent:_________
Value:__________________
Value:__________________
6.
2 4
7. (3)2
Base:_______ Exponent:_________
Base:_______ Exponent:_________
Value:__________________
Value:__________________
8.
(5)3 (8)3
Base:_______ Exponent:_________
9.
(13x)2
Base:_______ Exponent:_________
Base:_______ Exponent:_________
Value:__________________
10. (71y )5
Base:_______ Exponent:_________
11. 73 x 4
Base:_______ Exponent:_________
Base:_______ Exponent:_________
Write each power in expanded notation and evaluate to calculate the product.
13. 63
12. 43
Expanded Notation:______________________
Expanded Notation:______________________
Value:__________________
14. 32
Value:__________________
15. 75
Expanded Notation:______________________
Expanded Notation:______________________
Value:__________________
16. (8)3
Value:_________________
17. (3)4
Expanded Notation:______________________
Expanded Notation:______________________
Value:__________________
Value:__________________
Write each expression in expanded notation.
18. 32 x 4
19. 25 y 2
Expanded Notation:______________________
5 2
20. x z
Expanded Notation:______________________
21. 3x 2 z 4
Expanded Notation:______________________
22. 2a 3
Expanded Notation:______________________
23. (5 x)4
Expanded Notation:______________________
Expanded Notation:_____________________
25. 10  (2 xy) 4
24. (6 z )
3
Expanded Notation:______________________
Expanded Notation:______________________
Write each expression using exponents.
26. (7)(7)(7)(7)
27. 4  4  4  4  4  4
28. (3)(3)(3)(3)(3)
29. (6)(6)(6)(6)
30. 5  5  5
31. b  b  b  b  b  b  b
HW: 13.1C - Evaluating Exponents
Work down the page. Showing your work is REQUIRED! You can use calculator for powers and
multiplication, but you must show all steps.
1.
5 2  34
2.
33
3.
 2 
2
Work down the page. Showing your work is REQUIRED! You can use calculator for powers and
multiplication, but you must show all steps.
4.
5  2  83
4
6. 2  3
8.
 2  8
3
2
5. 4  (2)
7. 3  (4)2  23
3
9.
53  6  2
10. 2  32  23
12. (honors)
11.
2   32 
3
4  9  (6  2)
23  8
13. (honors) 2ab when a  5 and b  2
2
Powers – most common mistakes!
14. 5 4
3
2
15. (2) (5)
Base:_______ Exponent:_________
Expanded Notation:____________________________
Value:__________________
Value:__________________
17. 2  2  2  2  x  x  x  y  y  z
16. 4x
3
Expanded
Notation:______________________
Power:_______________________________________
HW: 13.1B
Problem Set
State the base and the exponent of each power. Then evaluate to find the value of the power.
1.
94
2. 182
Base:_______ Exponent:_________
Base:_______ Exponent:_________
Value:__________________
Value:__________________
4. (2a)5
3. (3z )5
Base:_______ Exponent:_________
Base:_______ Exponent:_________
Write each power in expanded notation and evaluate to calculate the product.
5. (6)6
6. (2)5
Expanded Notation:______________________
Expanded Notation:______________________
Value:__________________
Value:__________________
7. (4) 2 (5)3
8.
(2)5 (6)2
Expanded Notation:______________________
Expanded Notation:______________________
Value:__________________
Value:__________________
9. (3)6 (2) 4
10. (5)3 (9) 2
Expanded Notation:______________________
Expanded Notation:______________________
Value:__________________
Value:__________________
Write each expression in expanded notation.
11. (6 y )3
Expanded Notation:______________________
12. (4a)3
Expanded Notation:______________________
13. 8z 4
14. (3x) 2 y 4
Expanded Notation:______________________
Expanded Notation:______________________
16. (honors) (1)3 (ab2 )4
15. (honors) 15  (2 y 4 )3
Expanded Notation:______________________
Expanded Notation:______________________
Write each expression using exponents.
17.  z   z   z
18. t  t  t  t
19. ( x)( x)( x)( x)( x)
20. (10)(10)(7)(7)(7)(7)
21. 2( x)( x)( x)( x)( x)
22. 10 10  x  x  x  x  x  x  x
Write each expression using exponents.
23. ( x)( x)( x)( y )( y )
24. (a)(a)(a)(a)(a)(c)(c)(c)(c)(c)(c)
25. ( y )  ( y )  z  z  z  z  z
26. 4  4  4  4  4  m  m  m  m  n  n
27. 4a  4a  4a  2b  2b  2b  c  c  c
28. (2 x)  (2 x)  (2 x)  ( y)  ( y)  ( z )  ( z )
29. 2  3  3  3  m  m  m  m  m  n
30. (honors) 3  5  3  5  3  5  3