SOLUTION: Use the power rule and the power of a product or quotient rule to simplify the expresion (2p^3v^4/s^3)^3

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Question 116929: Use the power rule and the power of a product or quotient rule to simplify the expresion
(2p^3v^4/s^3)^3

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
%282p%5E3v%5E4%2Fs%5E3%29%5E3
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In order to simplify this you cube every factor in the parentheses:
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The factors inside the parentheses are 2, p^3, v^4, and s^3. Cubing the 2 results in 2*2*2 which
equals 8. In the other three factors you use the power rule which says that you multiply the
exponents of these factors by 3 to cube them. The exponent of p is 3 and when you multiply
that by 3 you get 9. The exponent of v is 4 and multiplying that by 4 gives 12. And finally,
the exponent of s is 3 and multiplying that by 3 gives 9. When you substitute those results
the problem becomes:
.
%288p%5E9v%5E12%2Fs%5E9%29
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And that's the simplification you are looking for.
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Hope this helps you to understand the use of the power rule in raising terms with exponents
to another power.
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