Negative Integer Exponents
Here is a summary of our work with negative exponents:
Definition |
Example 1 |
Example 2 |
![](./articles_imgs/790/negati3.gif) |
![](./articles_imgs/790/negati4.gif) |
![](./articles_imgs/790/negati5.gif) |
Here, the variables represent nonzero real numbers and n is a nonnegative
integer.
Example 1
Find:
![](./articles_imgs/790/negati6.gif)
Solution |
![](./articles_imgs/790/negati7.gif) |
Use the definition of a negative exponent,
![](./articles_imgs/790/negati8.gif) |
![](./articles_imgs/790/negati9.gif) |
Evaluate the exponential expressions. |
![](./articles_imgs/790/negati10.gif) |
In the denominator of the expression, write each
fraction using the LCD, 18. |
![](./articles_imgs/790/negati11.gif) |
In the denominator of the expression, subtract
the fractions.
|
![](./articles_imgs/790/negati12.gif) |
Rewrite the division using ÷.
|
![](./articles_imgs/790/negati13.gif) |
To divide 5 by a fraction, multiply
by the
reciprocal of the fraction.
|
![](./articles_imgs/790/negati15.gif) |
Multiply the numerators and multiply the denominators.
|
![](./articles_imgs/790/negati16.gif) |
Thus,
![](./articles_imgs/790/negati17.gif)
Example 2
Rewrite using only positive exponents:
![](./articles_imgs/790/negati18.gif)
Solution
Since -7 is the exponent of y, not 5y, 5y -7 =
5 · y -7 |
![](./articles_imgs/790/negati19.gif) |
Use the definition
|
![](./articles_imgs/790/negati21.gif) |
Thus,
![](./articles_imgs/790/negati22.gif)
|