Properties of Exponents

1
Properties of Exponents
Learn to apply the properties of exponents and to
evaluate the zero exponent.
2
The factors of a power, such as 74, can be
grouped in different ways. Notice the
relationship of the exponents in each product.
7 7 7 7 74
(7 7 7) 7 73 71 74
(7 7) (7 7) 72 72 74
3
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4
Multiplying Powers with the Same Base
Multiply. Write the product as one power.
Add exponents.
B. n5 n7
Add exponents.
5
Multiplying Powers with the Same Base Continued
Multiply. Write the product as one power.
C. 25 2
Add exponents.
D. 244 244
Add exponents.
6
Notice what occurs when you divide powers with
the same base.
7
Dividing Powers with the Same Base
Divide. Write the quotient as one power.
A.
Subtract exponents.
B.
Subtract exponents.
x
8
Try This
Divide. Write the quotient as one power.
9
9
A.
9
2
Subtract exponents.
97
e
10
B.
e
5
Subtract exponents.
9
When the numerator and denominator have the same
base and exponent, subtracting the exponents
results in a 0 exponent.
This result can be confirmed by writing out the
factors.
10
0
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12
Practice
Write the product or quotient as one power
1. n3 ? n42. 3.4. 33 32 355. 8
88

1. n7
2. 104
3. t2
4. 310
5. 89