1.2 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.

What you should learn

To solve real-life problems, such as finding the volume of a glass cube.

Why you should learn it

GOAL 1 EXPRESSIONS CONTAINING EXPONENTS

VOCABULARY

•power

•base

•exponent

1.2 Exponents and Powers

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:

exponentpower = base

Extra Example 1

EXAMPLE 2

Express the meaning of the power in words and then with numbers or variables. Click for the answers.

1. 81

2. 62

3. 43

4. 97

5. yn

EXAMPLE 1

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

Extra Example 2

EXAMPLE 3

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.

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

(3 + 4)3

73

343

You may use your calculator once you show your substitution.

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

Extra Example 4

Evaluate the expression when x = 5.

Click for the solutions.

1. 3x2 2. (3x)2

2

2

3

3(5)

75

x1. 2. 2

2

(3 )

(3 5)

225

x

Write

Substitute

Simplify

Checkpoint1. Express the meaning of 64 with numbers.

2. Find x5 when x = 4.

3. Evaluate each expression when a = 2 and b = 3.

(a + b)2 a2 + b2

4. Evaluate each expression when x = 2.

4x3 (4x)3

6•6•6•6

1024

25 13

32 512

GOAL 2 REAL-LIFE APPLICATIONS OF EXPONENTS

1.2 Exponents and Powers

EXAMPLE 5

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”).

Extra Example 5Make 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.

EXAMPLE 6

Side, s s2 Area

30 cm

40 cm

50 cm

900 900 cm2

1600 1600 cm2

2500 2500 cm2

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.

2. How many gallons of water will the cubic tank hold? (One cubic foot holds 7.48 gallons.)

3

3

3

(4.5 ft)

91.125 ft

V s

33

7.48 gal91.125 ft

1 ft

V

681.615 gal

4.5 ft

CheckpointFind 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.

3

3

5(3.1 cm)

148.955 cm

QUESTIONS?