Question 74072
{{{(-5/2a^3) ^3}}}
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There are a couple of ways that you can do this problem.  Remember that the definition of
cubing an expression. It means multiplying by itself 3 times as in:
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{{{(-5/2a^3)*(-5/2a^3)*(-5/2a^3) = (-5)*(-5)*(-5)/((2a^3)*(2a^3)*(2a^3))}}}. The numerator
multiplies out to {{{-5*-5*-5 = -125}}} and the denominator to {{{(2*2*2*a^3*a^3*a^3)= 8a^9}}}
Combining these results gives:  {{{-125/(8a^9)}}}
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The short hand method says that when you raise a fraction to a power, both the numerator
and denominator get raised to that power. So:
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{{{(-5/(2a^3))^3 = (-5)^3/(2a^3)^3 = (-5)^3/((2)^3*(a^3)^3)=(-125)/(8*a^9)}}}
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Hope this helps you to understand this problem.