How to do division when
(a power x) / (b power y)
Say, a,x,b,y are distinct values.
For example,
(2 power 19) / (7 power 23). Doing mathematical operations with bigger exponents is tedious and error-prone.
Is there any way to simplify above expression such that the final decimal result wouldn't change?
Is there any way to simplify this such that after simplifying, I don't have to calculate exponent > 10, say.
I had the same question posted in sof :
But the problem with that solution is I'm ending up calculating huge exponents even after simplifying.
Well, you could use the same trick, going calculation to the base you would like to see the answer. I assume base 10 for simplicity
$$ 2^{19 - 23\log_2{7}} = 10^{\log_{10}2\;(19 - 23\log_2{7})}=10^{-13.717685}=10^{0.282315}\;10^{-14}= 1.915645\;10^{-14} $$
You don't have to compute huge exponent ($10^{-14}$), it goes directly to output