Raising an Exponential Expression to a Power
When we raise an exponential expression to a power, we can use the product
rule to find the result, as shown in the following example:
| (w4 )3 |
= w4 · w4 · w4 |
Three factors of w4 because of the exponent 3 |
| |
= w12 |
Product rule |
By the product rule we add the three 4's to get 12, but 12 is also the
product of 4 and 3.
This example illustrates the power rule for exponents.
Power Rule
If m and n are nonnegative integers and a ≠ 0,
then (a m) n = a mn.
Example 1
Using the power rule
Use the rules of exponents to simplify each
expression. Assume that all vairables represent nonzero real numbers.
a) 3x2(x3 )5
b)
c)
Solution
| a) 3x2(x3
)5 |
= 3x2x15 |
Power rule |
| |
= 3x17 |
Product rule |
| b)
|
 |
Power rule and product rule |
| |
 |
Product rule |
| |
= 25 |
Quotient rule |
| |
= 32 |
Evaluate 25. |
c)
|
