Exponential Notation

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Exponential Notation
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Exponent Essential Question
How do we write numbers using exponents?
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Vocabulary
exponential form exponent base power
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If a number is in exponential form, the exponent
represents how many times the base is to be used
as a factor. A number produced by raising a base
to an exponent is called a power. 27 and 33 are
equivalent.
Exponent
Base
7
2
5
Additional Example 1 Writing Exponents
Write in exponential form.
A. 4 4 4 4
Identify how many times 4 is a factor.
B. (6) (6) (6)
Identify how many times 6 is a factor.
(6) (6) (6) (6)3
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Additional Example 1 Writing Exponents
Write in exponential form.
Identify how many times 5 and d are each used as
a factor.
C. 5 5 d d d d
5 5 d d d d 52d4
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Check It Out! Example 1
Write in exponential form.
A. x x x x x
Identify how many times x is a factor.
B. d d d
Identify how many times d is a factor.
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Check It Out! Example 1
Write in exponential form.
C. 7 7 b b
Identify how many times 7 and b are each used as
a factor.
7 7 b b 72b2
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Additional Example 2 Simplifying Powers
Simplify.
35 3 3 3 3 3
Find the product.
243
B.
Find the product.
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Additional Example 2 Simplifying Powers
Simplify.
Find the product.
256
Find the product. Then make the answer negative.
28 (2 2 2 2 2 2 2 2)
256
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Check It Out! Example 2
Simplify.
74 7 7 7 7
Find the product.
2401
Find the product.
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Check It Out! Example 2
Evaluate.
Find the product.
25
Find the product. Then make the answer negative.
94 (9 9 9 9)
6,561
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Exponent Essential Question
How do we use exponents within the order of
operations?
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In the Order of Operations
The order in which mathematicians perform math
problems.

1. Parenthesis working inward outward
2. Exponents
3. Multiply or Divide Left to Right
4. Add or Subtract Left to Right

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Mnemonic

• Please
• Parenthesis
• Excuse
• Exponents
• My Dear
• Multiply or Divide Left to Right
• Aunt Sally
• Add or Subtract Left to Right

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• 4 X 6 (3 4) 22

Parenthesis
4 x 6 - 7 22
Exponents
4 X 6 7 4
Multiply
24 7 4
Add or Subtract Left to Right
17 4
21
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Additional Example 3 Using the Order of
Operations

Substitute 4 for x, 2 for y, and 3 for z.
4(24 32) 42
4(16 9) 16
Simplify the powers.
4(7) 16
Subtract inside the parentheses.
Multiply from left to right.
28 16
Add.
44
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Check It Out! Example 3


Substitute 5 for x, 2 for y, and 60 for z.
60 7(25 52)
60 7(32 25)
Simplify the powers.
60 7(7)
Subtract inside the parentheses.
60 49
Multiply from left to right.
Subtract.
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Check It Out! Example 4
Use the expression (n2 3n) to find the
number of diagonals in a 4-sided figure.
Substitute the number of sides for n.
Simplify inside the parentheses.
Subtract inside the parentheses.
2 diagonals
Multiply