Algebra is the study of using symbols to express
mathematical ideas . The topic in this
lesson is dividing monomials . Negative exponents will be introduced as a way to
express
factors in the denominator .
Dividing with Exponents
Example:
In 1994, 532 billion cigarettes were sold in the United States. We would
write 532 billion as 532,000,000,000 or, using scientific notation, we
would write it as 5.32 x 1011.
In 1994 the Properties /adding-negative-numbers-on-ti.html">number of people in the U.S. 18 years old or older were 190
million. How many cigarettes sold per person in 1994?
If we write 190 million as 190,000,000 or 1.9 x 108, we can divide
the
number of cigarettes sold by the number of people to find out how many
cigarettes sold per person.
(5.32 x 1011) / (1.9 x 108) = (5.32 /1.9) x 103
= 2.8 x 103 = 2800, so in 1994
2800 cigarettes sold per person.
Notice how eight factors of 10 cancelled from the numerator and denominator . In
general, when we have like factors in the numerator and the denominator, we can
combine them by subtracting exponents .
| Subtracting exponents |
 |
Examples simplify
We can apply the rule of subtracting exp onents to each
different factor that appears in
both the numerator and the denominator of a fraction .
Example simplify
Example simplify
Worksheet
Worksheet with solutions
When factors remain in the denominator, we use negative
exponents
| Definition |
 |
Examples simplify and write without denominators
simplify and write without denominators
simplify and write without denominators
Fractions may be expressed both ways, either with negative
exponents or with
denominators. It is important that algebra students can express fractions both
ways.
When rewriting a factor with a negative exponent, move the factor to the other
part of the
fraction and remove the negative.
Examples write without negative exponents
write without negative exponents
write without negative exponents
write without negative exponents
Summary
| Definitions |
x0 = 1 |
| |
 |
| |
xnxk = xn+k |
| Properties |
 |
Worksheet
Simplify and write without negative
exponents. |
Solution |
| x2x3 |
|
| x2 + x3 |
|
| - 2(x3y)2 |
|
| -2x-3 |
|
| 3y-4 |
|
 |
|
| ( 3x 2 / 2y ) 4 |
|
| x2y-3 |
|
Worksheet with solutions
Simplify and write without negative
exponents. |
Solution |
| x2x3 |
x5 |
| x2 + x3 |
cannot simplify further |
| - 2(x3y)2 |
- 2(x3y)(x3y) = -2x6y2 |
| -2x -3 |
-2 / x3 |
| 3y-4 |
 |
 |
 |
 |
 |
| x2y-3 |
 |
cannot