Chipola College
MGF 1107
5.6 Rules of Exponents and Scientific Notation
A. Negative powers indicate reciprocals. Simplify the following.
1. 2
-3
4. 5
-2
=
=
1
2
3

1
8
2. 3
-3
= 3. 4
-2
=
5. 8
-1
= 6. 1
3

3

B. A power equal to zero indicates a value of 1 . Evaluate. Ex. 8 0 = 1; -6y 0 = -6

1
 
6
1. 4
0
= 2. 8
0
= 3. 3x
0
= 4. -5
0
=
C. To multiply exponential expressions add the exponents. Multiply expressions.
1. 3

3 
3
7 
2. 5
-4
(5) = 3. 2
3 
2
2
D. To divide exponential expressions subtract the exponents. Note – you may want to write the expression
using positive exponents first. Divide the following expressions.
1.
6
5
6
3
 2.
8
9
E. To raise an exponential expression to a power multiply the exponents. Ex.
 
3  x
12
You Try:
1. (7
3
)
4
=
4. (5
-3
)
2
=
2. (3
5
)
2
=
5. (-2)
4
3. (3
-4
)
-5
=
6. (-345
72
)
0
2 a. - 3
2
b. (-3)
2 c.
3
4 d. (2
2
)
-3
e.
7
7
3 f. 4
5 
4
3

Scientific Notation
Often scientific problems deal with very large and very small numbers. Thus, we need a “shorter” way to write them. Very small numbers are written using negative exponents. Very large numbers are written using positive exponents.
1.
Write the following numbers in scientific notation.
______________ a. half-life of lead 14,000,000,000,000,000,000 yrs
______________ b. mass of earth 5,980,000,000,000,000,000,000,000 kgs
______________ c. wavelength of yellow-green light .0000006 meters
______________ d. mass of hydrogen .000 000 000 000 000 000 001 067 g
2.
Convert the following into standard or decimal notation.
_______________ a. 7.84 X 10
5
_______________________ b. 5.3 X 10
-3
________________ c. 6 X 10
-6
________________ e. 4.58 X 10
2
_______________________ d. 2 X 10
6
________________________f. 3.7 X 10
-1
You Try:
Fill in the blanks. STANDARD
5230000
__________
__________
SCIENTIFIC
__________
7.82 X 10
-4
4.367 X 10
3
.00000078 __________
___________
.0249
6.55 X 10
___________
__________ 2 X 10
5
__________ 7 X 10
-5

Multiplying and Dividing using Scientific Notation
Multiply or divide. Write your answers in standard notation and scientific notation.
1. (3 X 10 4 )(2 X 10 2 ) 2. (1.2 X 10 -7 )(3.1 X 10 2 )
3.
7 .
8 X 10
9
4 X 10
3
4.
5 .
6 X 10

4
2 .
5 X 10
3
5. (0.000041)(3000) 6. 0 .
0000000000 48
24 , 000 , 000 , 000
You Try: a. (4 X 10
3
)(7 X 10
5
)
3 X 10
8 c.
6 X 10
12 b. (3.2 X 10
-7
)(4 X 10
3
) d.
3 .
2 X 10

5
8 .
0 X 10

8
e. (0.000041)(3000) f.
20 , 000
0 .
0005