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.




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.



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