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Pre-Algebra
Powers and Exponents
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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.
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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.
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Vocabulary Words
Factors—Two or more numbers multiplied together to form a product.
Example—2 • 3 = 6 The numbers 2 and 3 are
factors.
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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
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Vocabulary
Base—The common factor or number being multiplied.
5 • 5 • 5 • 5 • 5 Five is the base
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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.”
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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
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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
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Write each expression in exponential form.
a. 6 · 6 · 6 b. (-3)(-3)(-3)(-3)
c. (-4n)(-4n)(-4n)(-4n)(-4n)
d. 4 · y · x · y · 3 · x · y
e. 9 · (p + 1)(p +1)
f. -5 · x · x · y · y · x
g. (a + 1)(a +1)(a +1)
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Write each expression in exponential form.-8 • n • n • n • 4 • t
-32n
3t
-32
• 3n •
t
-8n3
+ 4
t
-32n
t3
25% 25%25%25%
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
1. -32n3t2. -32 • 3n • t3. -8n3 + 4t4. -32nt3
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Vocabulary
Evaluate—Find the value of an expression.
Standard Form—Numbers written without exponents.
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Write Powers in Standard Form
Evaluate each expression.
Example 1 -- 2 to the fifth power = 2 · 2 · 2 · 2 · 2 = 32
Example 2-- 4³ = 4 · 4 · 4 = 64
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Evaluate each expression.
a. 7³
b. 52
c. (-4)³
d. -8²
e. 3 · 4²
f. 4² · 5³
g. 2³ · 5² · 7
h. 3 · 5² + 2³ · 3²
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Evaluate.-32
-9 9 6 -6
25% 25%25%25%
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
1. -92. 93. 64. -6
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Evaluate each expression
a. 5² · 8² · 3³
b. 9 · 6² · 2 · 3³
c. 3(2 • 2 + 5)²
d. 6² + 2(6) + 5
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Evaluate. 12 - 42
-4
12
– 4
• 4 4
12
- 16
25% 25%25%25%
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
1. -42. 12 – 4 • 43. 44. 12 - 16
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Determine whether each pair of expression is equivalent. Write yes or no.
a. 4ab2 and 4(ab)2
b. (2x)³ and 8x³
c. (mn)4 and m4 • n4
d. c³d³ and cd³
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Compare using <, >, or =.a. 3³ 5²
b. 4³ 8²
c. 64÷8 2³
d. 4•10 102
e. -5³ -3°
f. 35 4³
g. -10³ (-10)³
h. 5² 23
i. 6³ 42
j. 24 4²
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Class Work
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