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# 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 Â· 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