Raising a Product to a
Power
Consider how we would simplify a product raised to a positive power and a product
raised to a negative power using known rules.
In each of these cases the original exponent is applied to each factor of the product.
These examples illustrate the power of a product rule.
Power of a Product Rule
If a and b are nonzero real numbers and n is any integer, then
(ab)n = an · bn.
Example
Using the power of a product rule
Simplify. Assume the variables represent nonzero real numbers. Write the answers
with positive exponents only.
a) (-3x)4
b) (-2x2)3
c) (3x-2y3)-2
Solution
| a) (-3x)4 |
= (-3)4x4 |
Power of a product rule |
| |
= 81x4 |
|
| b) (-2x2)3 |
= (-2)3(x2)3 |
Power of a product rule |
| |
= -8x6 |
Power of a power rule |
|
