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December 17th, 2015, 02:29 AM  #1 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7  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. 
December 17th, 2015, 02:54 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,386 Thanks: 2012 
Hint: $\displaystyle \large\frac{10^{3n/2}\times15^{n/2}\times6^{n/6}}{45^{n/3} \times 20^{2n/3}} = \frac{2^{3n/2}5^{3n/2}\times3^{n/2}5^{n/2} \times 2^{n/6}3^{n/6}}{3^{2n/3}5^{n/3} \times 2^{4n/3}5^{2n/3}}$.

December 18th, 2015, 01:43 AM  #3 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7 
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. 
December 18th, 2015, 01:54 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,386 Thanks: 2012 
You can simplify the first exponent in your answer by cancelling 2. When evaluating the expression for $n$ = 2, you should not change × to +. 
December 18th, 2015, 02:18 AM  #5 
Senior Member Joined: Jan 2012 Posts: 725 Thanks: 7 
I have edited the post. I hope things are right now.


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