Powers of Products MathBitsNotebook.com
 For all numbers x and y and integers n,
 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) When in doubt, expand terms to see what is happening.

Examples:

 1.  (3 x 5)3 = 33 x 53 = 3375 Notice that the interior of the parentheses is a product (the multiplication of two terms). Each term is raised to the power of 3. 2.  (32 x 26)4 = 38 x 224 Apply the "power to a power" rule, as well as this power of products rule. 3.  (72 x 11 x 23)5 = 710 x 115 x 215 Since the interior of the parentheses is a product, each term gets raised to the power of 5. Remember the rule for a "power to a power". 4.  (abc)4 = a4b4c4 The variables abc are a product a•b•c, so apply the rule to each factor. 5.  (5a)5 = 55a5 = 3125a5 Notice how the 5 inside the parentheses is also affected by the power of 5. 6.  (3a2)4 = 34(a2)4 = 34a8 = 81a8 Notice how the "power to a power" rule was used here to raise a2 to the power of 4. 7.  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. 8.  P = (2K)2W = 22K2W = 4K2W Formulas often involve working with powers.