Download Powers and Exponents Practice 2

Name: ________________________ Class: _________________
Bases and Exponents Practice II
o I can solve problems involving powers
o I can explain and apply all of the exponent laws
o I can use the order of operations on expressions with powers
1. Write each expression as a single power and then evaluate.
a) 6 4  6 3
b) (11) 7  (11) 5
c)
3 4  35
33
d)
56
53  5
e)
(4) 3  (4) 6
(4) 2  (4) 4
f)
10 6  10 0
10 3  10 2
2. Why do you add the exponents to simplify the expression 3 2  3 4 but multiplying the exponent to
simplify the expression (32 ) 4 ?
3. Write each expression as a product of powers:
Expression
a) (6  4) 3
Product of Powers
Expression
b) (2  5) 4
c) {( 2)  3)}5
d) (25  4) 2
e) (11 3)1
f) {( 3)  (4)}3
4. Write each expression as a single power:
Product of Powers
Name: ________________________ Class: _________________
Expression
a) (32 ) 4
Single Power
Expression
b) (6 3 ) 3
c) (5 3 )1
d) (7 6 ) 0
e)  (8 2 ) 2
f) {(3) 4 }2
5. Simplify each expression. Then evaluate.
a) (2 2 ) 4
b) - (33 ) 3
c) {(5) 2 }3
d) (9  4) 2
e) {( 2)  3)}3
f) - (3  4) 2
6. Evaluate:
a) 3 4  3 2
c) 10 3  10 2
7. Simplify each expression. Then evaluate.
b) (4) 2  (4) 3
d) (5) 4  (5) 2
Single Power
Name: ________________________ Class: _________________
a) (32  31 ) 2
b) (4 6  4 4 ) 2
c) (12 2 ) 4  (12 3 ) 2
d) {( 2) 0  (2) 3 }2
e) (10 6  10 4 ) 3
f)
8. Simplify each expression. Then evaluate.
a) 3  2 3  8  4
(5 2 ) 6  (53 ) 4
b) (2 3 ) 4  (2 4  2 3 ) 2
c) (4  2) 4  (53 ) 2
d) 2 3  (5  2) 4
e) (23  2 6 ) 2  (37  35 ) 4
f) {( 4) 3  (4) 2 }2  (4 2 ) 2
Name: ________________________ Class: _________________
9. An alfalfa field is a rectangle, 10 4 m long and 10 3 wide. Write an expression for the area of the
alfalfa field. Then evaluate.
10. A type of bacteria is known to double every hour. There are 50 bacteria to start with. How many
will there be after:
a) 3 hours
b) 9 hours
c) 15 hours
11. A standard combination lock has 40 numbers on its face from 0 to 39. A combination consists of
three numbers, and numbers can be repeated. What is the total number of possible combinations?
Express as a power and then evaluate.
12. A white square with a side length of 8 cm is placed on a black square with a side length of 10 cm.
a) Write an expression with powers to determine the visible black area.
b) What is the visible black area?