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 will be raised to the power of 3.
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2. (32 x 26)4 = 38 x 224
You have a product inside the parentheses. So raise each term in the product to a power of 4. Since each term has an exponent, you must also apply the "rule to raise a power to a power" (when tells you to multiply the powers). 
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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".
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4. (abc)4 = a4b4c4
The variables abc are a product a•b•c, so apply the rule to each factor.
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5. (5a)5 = 55a5 = 3125a5
Careful!!! The value inside the parentheses is actually 5 x a. So BOTH the 5 and the a will be raised to a power of 5. |
6. (3a2)4 = 34(a2)4 = 34a8 = 81a8
The "power to a power" rule is used again here to raise a2 to the power of 4. Don't forget to raise the 3 to a power of 4.
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7. 4(2x3)2 = 4•22(x3)2 = 4•4•x6 = 16x6
Sneaky!! Notice that the number 4 out in front is not affected by the power of 2 since it is not within the parentheses.
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8. P = (2K)2W = 22K2W = 4K2W
Formulas often involve working with powers.
Again, don't forget to raise the 2 to a power of 2.
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