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Math 010 - Cooley
Elementary Algebra
OCC
Section 4.8 – Negative Exponents and Scientific Notation
Negative Exponents
For any real number a that is nonzero and any integer n,
a n 
1
an
(The numbers a  n and a n are reciprocals of each other.)
Factors and Negative Exponents
For any nonzero real numbers a and b and any integers m and n,
a n b m

b m a n
(A factor can be moved to the other side of the fraction bar if the sign of the exponent is changed.)
Reciprocals and Negative Exponents
For any nonzero real numbers a and b and any integer n,
n
n
a
b
   
b
a
(Any base to a power is equal to the reciprocal of the base raised to the opposite power.)
Scientific Notation
Scientific notation for a number is an expression of the type,
N  10 m ,
where N is at least 1 but less than 10 (that is, 1  N  10 ), N is expressed in decimal notation, and m is an integer.
 Exercises:
Express using positive exponents. Then, if possible, simplify.
1)
5)
2 4
3
1
2)
5 3
6)
3
 
4
3)
(3) 4
7)
x
 
2
11)
y 5  y
2
4)
xy 9
8)
r
 
v
12)
x 
4
5
Simplify. Do not use negative exponents in the answer.
9)
5 8  510
10)
x 2  x 9
5 6
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Math 010 - Cooley
Elementary Algebra
OCC
Section 4.8 – Negative Exponents and Scientific Notation
 Exercises:
Simplify. Do not use negative exponents in the answer.
13)
4x
17)
5 x 8
y 3 z 2
5
y 6

3
16)
8a 6
2a 10
20)
( x 3 y 4 z 5 )( x 4 y 2 z 9 )
9.043  10 3
24)
7.26  10 4
27)
370,000,000
28)
0.00000000952
30)
3  10 7
6  1012
14)
x7
x 2
15)
z 6
z 2
18)
( x 2 y 7 ) 5
19)
 4a 3 b  2

 5c 3

1.35  10 7
23)
0.0814




2
Convert to decimal notation.
21)
8.92  10 2
22)
Convert to scientific notation.
25)
71,500
26)
Multiply or divide, and write scientific notation.
29)
(1.9  10 8 )(3.4  10 3 )
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