Powers of Products

Powers of Products

Rule: For all numbers x and y , and integers n,
“Notice: each factor of the product gets raised to the new power.”
“Be sure to notice that this rule ONLY works when the inside of the parentheses is a single term (a product). ”
“(no + signs or – signs separating the items).”
Consider:

Check out these examples of this rule at work:

1. (4a)⁴ = 4⁴a⁴ = 256a⁴
   Notice how the 5 inside the parentheses is also affected by the power of 5.
2. (2a²)⁴ = 2⁴(a²)⁴ = 2⁴a⁸ = 16a⁸
   Notice how the “power to a power” rule was used here to raise a² to the power of 4.
3. 4(2x³)² = 4•2²(x³)² = 4•4•x⁶ = 16x⁶
   Notice that the number 4 out in front is not affected by the power of 2 since it is not within the parentheses.
4. P = (2K)²W = 2²K²W = 4K²W
   Formulas often involve working with powers.