1. Pre-Algebra
Powers and Exponents

2. What Are You Learning?
I CAN write powers as a product of the same factor and
I CAN write products in exponential form.
I CAN evaluate exponents.

3. Why Do You Need To Know This?
Exponents are used in the real-world to represent extremely large and small numbers. They are also used in solving problems.

4. Vocabulary Words
Factors—Two or more numbers multiplied together to form a product.
Example—2 • 3 = 6
The numbers 2 and 3 are factors.

5. Vocabulary
Exponent—Number that tells how many times the base is used as a factor.
4²--2 is the exponent and it shows that 4 will be multiplied two times. 4 • 4

6. Vocabulary
Base—The common factor or number being multiplied.
5 • 5 • 5 • 5 • Five is the base

7. Vocabulary Powers—Numbers expressed using exponents
4² and 6³ are examples of powers.
4² is read “four to the second power.”
6³ is read “six to the third power.”

8. Vocabulary Squared—A number multiplied by itself two times.
4 x 4 or 4² The four is being squared.
Cubed—A number multiplied by itself three times.
2 x 2 x 2 or 2³

9. Write Numbers in Exponential Form
Exponential Form—Numbers written with exponents.
Example 1—Write (-5)(-5)(-5) in exponential form.
-5 is the base. It is used as a factor 3 times. So, the exponent is 3.
(-5)(-5)(-5) = (-5)³

10. Write each expression in exponential form.
6 · 6 · 6
(-3)(-3)(-3)(-3)
(-4n)(-4n)(-4n)(-4n)(-4n)
4 · y · x · y · 3 · x · y
9 · (p + 1)(p +1)
-5 · x · x · y · y · x
(a + 1)(a +1)(a +1)

11. Write each expression in exponential form. -8 • n • n • n • 4 • t1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

12. Vocabulary
Evaluate—Find the value of an expression.
Standard Form—Numbers written without exponents.

13. Write Powers in Standard Form
Evaluate each expression.
Example to the fifth power =
2 · 2 · 2 · 2 · 2 = 32
Example 2-- 4³ = 4 · 4 · 4 = 64

14. Evaluate each expression.7³ 52
(-4)³
-8²
3 · 4²
4² · 5³
2³ · 5² · 7
3 · 5² + 2³ · 3²

15. Evaluate. -32 -9 9 6 -6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

16. Evaluate each expression
5² · 8² · 3³
9 · 6² · 2 · 3³
3(2 • 2 + 5)²
6² + 2(6) + 5

17. Evaluate -4
12 – 4 • 4 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

18. 4ab2 and 4(ab)2 (2x)³ and 8x³ (mn)4 and m4 • n4 c³d³ and cd³
Determine whether each pair of expression is equivalent. Write yes or no.
4ab2 and 4(ab)2
(2x)³ and 8x³
(mn)4 and m4 • n4
c³d³ and cd³

19. Compare using <, >, or =.
3³ 5²
4³ 8²
64÷ ³ 4•
-5³ ° ³
-10³ (-10)³ 5² 6³ ²

20. Class Work