1. 1.2 Exponents and Powers
Algebra 1 Concepts and Skills McDougal Littell Linda Stamper

2. An expression like 43 is called a power.
base 
 exponent
word form: four to the third power
four cubed
factor form (meaning): 4 • 4 • 4
evaluated form: 64

3. Example 1 Express the power in words. Then write the meaning.
1. Write problem. 82
2. Write word form.
eight squared
3. Write meaning.
(factored form)
8 • 8

4. 53 Example 2 Express the power in words. Then write the meaning.
1. Write problem. 53
2. Write word form.
five cubed
3. Write meaning.
5 • 5 • 5

5. Example 3 Express the power in words. Then write the meaning.
1. Write problem. y4
y to the fourth power
2. Write word form.
3. Write meaning.
y • y • y • y

6. A power applies only to what is directly in front of it.
Evaluate when x = 6.
The problem. x2
Substitute.
(6)2
Write factors.
(6)(6)
Simplify. 36
You could write in factored form and then substitute. x2
(6)(6) 36

7. Example 4 Evaluate when m = 4 and n = 3.
When you evaluate exponential expressions, work within grouping symbols first.
( )
, [ ]
,{ }
Example 4 Evaluate when m = 4 and n = 3.
Remember: In algebra work downward. Highlight or circle your answer. Skip one line after the answer.
1. Write problem.
(m + n)2
2. Substitute.
((4) + (3))2
3. Simplify within
parentheses.
(7)2 49
4. Evaluate power.

8. When parentheses are nested work from the inside going out.
When you evaluate exponential expressions, work within grouping symbols first.
( )
, [ ]
,{ }
Example 5 Evaluate when m = 4 and n = 3.
(m2) + (n2)
1. Write problem.
((4)2) + ((3)2)
2. Substitute.
3. Write factors.
(4 • 4) + (3 • 3) Optional Step
4. Simplify within parentheses.
16 + 9 25
5. Simplify.
When parentheses are nested work from the inside going out.

9. Remember a power applies only to what is directly in front of it!
Example 6 Evaluate when a = 5.
Remember a power applies only to what is directly in front of it!
1. Write problem.
2a2
2. Substitute.
2(5)2
3. Evaluate power.
2(25)
4. Simplify. 50

10. Example 7 Evaluate when a = 5.
1. Write problem.
(2a)2
2. Substitute.
(2(5))2
3. Simplify within
parentheses.
(10)2
100
4. Evaluate power.

11. This cannot be written as 5123 inches!
Example 8 A box has the shape of a cube. Each edge s is 8 inches long. Find the volume in cubic inches.
1. Write formula.
V = s3
2. Substitute.
= (8)3
3. Write factors.
Optional Step
= 8 • 8 • 8
4. Simplify.
= 512
5. Write a sentence.
The volume of the box is 512 cubic inches.
This cannot be written as 5123 inches!

12. Homework
1-A2 Pages 12-14, # 1-57