Learn to evaluate expressions with exponents.

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Learn to evaluate expressions with 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. Both 27 and 33
represent the same power.
Exponent
Base
7
2
5
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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Example 1
Write in exponential form.
Identify how many times 5 and d are used as a
factor.
C. 5 5 d d d d
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You Try!
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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You Try!
Write in exponential form.
C. 7 7 b b
Identify how many times 7 and b are used as a
factor.
7 7 b b 72b2
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Example 2
Evaluate.
Find the product of five 3s.
35 3 3 3 3 3
243
Find the product of five 3s.
243
Helpful Hint
Always use parentheses to raise a negative number
to a power.
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You Try!
Evaluate.
Find the product of four 4s.
256
Find the product of eight 2s.
28 2 2 2 2 2 2 2 2
256
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Example 3 Using the Order of Operations


Substitute 4 for x, 2 for y, and 3 for z.
4(24 32) 42
Evaluate the exponent.
4(16 9) 16
Subtract inside the parentheses.
4(7) 16
Multiply from left to right.
28 16
Add.
44
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You Try!


Substitute 5 for x, 2 for y, and 60 for z.
60 7(25 52)
60 7(32 25)
Evaluate the exponent.
60 7(7)
Subtract inside the parentheses.
60 49
Multiply from left to right.
Subtract.
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Example 4 Geometry Application
Use the formula (n2 3n) to find the number
of diagonals in a 7-sided figure.
Substitute the number of sides for n.
Evaluate the exponent.
Multiply inside the parentheses.
Subtract inside the parentheses.
14 diagonals
Multiply
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Example 4 (continued)
A 7-sided figure has 14 diagonals. You can verify
your answer by sketching the diagonals.
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Check It Out Example 4
Use the formula (n2 3n) to find the number
of diagonals in a 4-sided figure.
Substitute the number of sides for n.
Evaluate the exponents.
Multiply inside the parentheses.
Subtract inside the parentheses.
2 diagonals
Multiply.
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Check It Out Example 4
A 4-sided figure has 2 diagonals. You can verify
your answer by sketching the diagonals.