1.2 Exponents and Powers
What you should learn
GOAL
1
Evaluate expressions containing exponents.
GOAL
2
Use exponents in real-life applications such
as finding the volume of an aquarium.
Why you should learn it
To solve real-life problems, such as finding the
volume of a glass cube.
1.2 Exponents and Powers
GOAL
1
EXPRESSIONS CONTAINING EXPONENTS
VOCABULARY
The expression 23 is called a power
_____.
•power
base and 3 is the _________.
exponent
2 is the _____,
•base
The exponent tells you how many times
the base is used as a factor.
•exponent
For this example, 23 = 2•2•2.
Remember:
power = baseexponent
Extra Example 1
Express the meaning of the power in words and then with
numbers or variables. Click for the answers.
1. 81
8 to the first power; 8
2. 62
6 to the second power (or 6 squared); 6•6
3. 43
4 to the third power (or 4 cubed); 4•4•4
4. 97
9 to the 7th power; 9•9•9•9•9•9•9
5. yn
y to the nth power; y•y•y•y•…•yn
EXAMPLE 1
EXAMPLE 2
Extra Example 2
Evaluate the expression x4 when x = 3.
Click for the solution.
Write:
x4
Substitute:
34
Simplify:
81
This is what I will
expect to see in all of
your written work!
When an expression contains grouping symbols,
remember to perform operations within the innermost set
first, then work your way to the outside, always following
the order of operations.
EXAMPLE 3
Extra Example 3
Evaluate the expression when a = 3 and b = 4.
1. (a + b)3
2. a + (b)3
Click to see the solutions.
1. (a + b)3 You may
2. a + (b)3
use your
3
(3 + 4) calculator
3 + 43
once you
73
3 + 64
show your
343
67
substitution.
Remember: An exponent only applies to the expression
immediately on its left. Take a look at
EXAMPLE 4
Extra Example 4
Evaluate the expression when x = 5.
Click for the solutions.
1. 3x2
2. (3x)2
1. 3 x 2
2. (3 x )2
3(5)2
75
Write
Substitute
Simplify
(3 5)2
225
Checkpoint
1. Express the meaning of 64 with numbers.
6•6•6•6
2. Find x5 when x = 4.
1024
3. Evaluate each expression when a = 2 and b = 3.
(a + b)2
25
a2 + b2
13
4. Evaluate each expression when x = 2.
4x3
(4x)3
32
512
1.2 Exponents and Powers
GOAL
2
REAL-LIFE APPLICATIONS OF EXPONENTS
One of the most common applications of exponents is in
finding the size of something, either in area or volume. You
should know the formula for the area of a square (A = s2)
and the volume of a cube (V = s3).
Note how to read units of area (ft2 is “square feet”) and
units of volume (cm3 is “cubic centimeters”).
EXAMPLE 5
Extra Example 5
Make a table showing the area of a square with side lengths
30 cm, 40 cm, 50 cm by using the formula A = s2.
Click for a hint, then click again for the solution.
Side, s
s2
Area
30 cm
900
900 cm2
40 cm
1600
1600 cm2
50 cm
2500
2500 cm2
EXAMPLE 6
Extra Example 6
A tank has the shape of a cube. Each edge is 4.5 feet long.
1. Find the volume in cubic feet.
V  s3
4.5 ft
 (4.5 ft)3
 91.125 ft 3
2. How many gallons of water will the cubic tank hold? (One
cubic foot holds 7.48 gallons.)
 7.48 gal 
V  91.125 ft 

3
1
ft


 681.615 gal

3

Checkpoint
Find the total volume of 5 cubes that all have the edge length
3.1 cm.
Click for a hint.
3.1 cm
V = 5s3
Click for the rest of
the solution.
 5(3.1 cm)3
 148.955 cm3
QUESTIONS?