Rules for Integral Exponents
In the next example we use the power rules with negative exponents.
Example
The power rules for integral exponents
Simplify each expression. Write your answers with positive exponents only.
Assume that all variables represent nonzero real numbers.
Solution
| a) (a-3)2 |
= a-3 · 2 = a -6
 |
Power rule
Definition of negative exponent |
| b) (10x -3) -2 |
= 10 -2(x -3)-2 = 10
-2x (-3)(-2)
 |
Power of a product rule Power rule
Definition of negative exponent
|
c) |
Power of a quotient rule Power of a product rule and
power rule
Because
Definition of negative exponent
Simplify |