1. 1.2 What you should learn Why you should learn it Exponents and Powers
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.

2. 1.2 Exponents and Powers 1 GOAL EXPRESSIONS CONTAINING EXPONENTS
VOCABULARY
power
base
exponent
The expression 23 is called a _____.
2 is the _____, and 3 is the _________.
The exponent tells you how many times the base is used as a factor.
For this example, 23 = 2•2•2.
power
base
exponent
Remember:

3. Extra Example 1
Express the meaning of the power in words and then with numbers or variables. Click for the answers. 81
2. 62
3. 43
4. 97
5. yn
8 to the first power; 8
6 to the second power (or 6 squared); 6•6
4 to the third power (or 4 cubed); 4•4•4
9 to the 7th power; 9•9•9•9•9•9•9
y to the nth power; y•y•y•y•…•yn
EXAMPLE 1
EXAMPLE 2

4. 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

5. Extra Example 3 Evaluate the expression when a = 3 and b = 4.
(a + b) a + (b)3
Click to see the solutions.
You may use your calculator once you show your substitution.
1. (a + b)3
(3 + 4)3 73
343
2. a + (b)3
3 + 43
3 + 64 67
Remember: An exponent only applies to the expression immediately on its left. Take a look at
EXAMPLE 4

6. Extra Example 4 Evaluate the expression when x = 5.
Click for the solutions.
1. 3x (3x)2 1.
Write
Substitute
Simplify 2.

7. Checkpoint Express the meaning of 64 with numbers. Find x5 when x = 4.
Evaluate each expression when a = 2 and b = 3.
(a + b)2 a2 + b2
Evaluate each expression when x = 2.
4x (4x)3
6•6•6•6
1024 13 25 32
512

8. 1.2 Exponents and Powers 2 GOAL 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

9. 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
40 cm
50 cm
900
900 cm2
1600
1600 cm2
2500
2500 cm2
EXAMPLE 6

10. Extra Example 6
A tank has the shape of a cube. Each edge is 4.5 feet long.
Find the volume in cubic feet.
How many gallons of water will the cubic tank hold? (One cubic foot holds 7.48 gallons.)
4.5 ft

11. 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.

12. QUESTIONS?