Download Powers and Exponents - Simpson County Schools

Pre-Algebra
Powers and Exponents
1
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.
2
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.
3
Vocabulary Words



Factors—Two or more numbers
multiplied together to form a
product.
Example—2 • 3 = 6
The numbers 2 and 3 are factors.
4
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
5
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
8
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
9
Write each expression in
exponential form.
a.
6·6·6
e.
9 · (p + 1)(p +1)
b.
(-3)(-3)(-3)(-3)
f.
-5 · x · x · y · y · x
c.
(-4n)(-4n)(-4n)(-4n)(-4n)
g.
(a + 1)(a +1)(a +1)
d.
4·y·x·y·3·x·y
10
Write each expression in exponential
form.
-8 • n • n • n • 4 • t
25% 25% 25% 25%
1
2
3
4
5
6
7
8
9
10
11
12
13
21
22
23
24
25
26
27
28
29
30
31
32
33
14
2n
t3
+
-3
n3
-3
2
-3
•3
n
2n
3t
4.
-8
3.
•t
2.
4t
-32n3t
-32 • 3n • t
-8n3 + 4t
-32nt3
1.
15
16
17
18
19
20
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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
13
Evaluate each expression.
7³
e.
3 · 4²
b.
52
f.
4² · 5³
c.
(-4)³
g.
2³ · 5² · 7
d.
-8²
h.
3 · 5² + 2³ · 3²
a.
14
Evaluate.
2
-3
25%
25%
25%
25%
-9
4.
1
2
3
4
5
6
7
8
9
10
11
12
13
21
22
23
24
25
26
27
28
29
30
31
32
33
14
15
16
-6
3.
6
2.
9
-9
9
6
-6
1.
17
18
19
20
15
Evaluate each expression
a.
5² · 8² · 3³
b.
9 · 6² · 2 · 3³
c.
3(2 • 2 + 5)²
d.
6² + 2(6) + 5
16
Evaluate.
2
12 - 4
25%
25%
25%
25%
-4
12 – 4 • 4
4
12 - 16
1.
2.
3.
4.
-4
12
1
2
3
4
5
6
7
8
9
10
11
12
13
21
22
23
24
25
26
27
28
29
30
31
32
33
14
–
4
•4
15
4
12
16
17
-1
6
18
19
20
17
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
18
Compare using <, >, or =.
a.
3³
5²
f.
35
b.
4³
8²
g.
-10³
c.
64÷8
2³
h.
5²
23
d.
4•10
102
i.
6³
42
e.
-5³
j.
24
4²
-3°
4³
(-10)³
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Class Work
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