1. (3 x 5)^{3} = 3^{3} x 5^{3} = 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. (3^{2} x 2^{6})^{4} = 3^{8 }x 2^{24}
Apply the "power to a power" rule, as well as this power of products rule.

3. (7^{2} x 11 x 2^{3})^{5} = 7^{10 }x 11^{5 }x 2^{15}
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} = a^{4}b^{4}c^{4}
The variables abc are a product a•b•c, so apply the rule to each factor.

5. (5a)^{5} = 5^{5}a^{5} = 3125a^{5}
Notice how the 5 inside the parentheses is also affected by the power of 5. 
6. (3a^{2})^{4} = 3^{4}(a^{2})^{4} = 3^{4}a^{8} = 81a^{8}
Notice how the "power to a power" rule was used here to raise a^{2} to the power of 4.

7. 4(2x^{3})^{2} = 4•2^{2}(x^{3})^{2} = 4•4•x^{6} = 16x^{6}
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)^{2}W = 2^{2}K^{2}W = 4K^{2}W
Formulas often involve working with powers.
