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December 17th, 2015, 02:29 AM   #1
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Simplify the expression

Simplify the expression
$\frac{10^{3n/2}\times15^{n/2}\times6^{n/6}}{45^{n/3}\times20^{2n/3}}$
and hence find its value when n = 2.
The challenge I am facing here is that I can't find a common factor or base for the numerator and denominator of the given problem. Could somebody help me out?

Last edited by Chikis; December 17th, 2015 at 02:42 AM.
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December 17th, 2015, 02:54 AM   #2
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Hint: $\displaystyle \large\frac{10^{3n/2}\times15^{n/2}\times6^{n/6}}{45^{n/3} \times 20^{2n/3}} = \frac{2^{3n/2}5^{3n/2}\times3^{n/2}5^{n/2} \times 2^{n/6}3^{n/6}}{3^{2n/3}5^{n/3} \times 2^{4n/3}5^{2n/3}}$.
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December 18th, 2015, 01:43 AM   #3
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When I finished simplifying, I got it in the most simplified form as $2^{n/3}\times5^n$. What do you think about the answer?
When n=2, the value of the expression becomes $2^{2/3}\times25$.

Last edited by skipjack; December 18th, 2015 at 03:28 AM.
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December 18th, 2015, 01:54 AM   #4
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You can simplify the first exponent in your answer by cancelling 2.

When evaluating the expression for $n$ = 2, you should not change × to +.
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December 18th, 2015, 02:18 AM   #5
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I have edited the post. I hope things are right now.
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