Question:১৫.প্রমাণ কর: `(x^a/x^b)^(1/(ab)) . (x^b/x^c)^(1/(bc)) . (x^c/x^a)^(1/(ca)) = 1`
Answer সমাধান: বামপক্ষ `= (x^a/x^b)^(1/(ab)) . (x^b/x^c)^(1/(bc)) . (x^c/x^a)^(1/(ca)) ` `= (x^(a - b))^(1/(ab)) . (x^(b - c))^(1/(bc)) . (x^(c - a))^(1/(ca))` `= x^((a - b)/(ab)) . x^((b - c)/(bc)) . x^((c - a)/(ca))` `= x^((a - b)/(ab) + (b - c)/(bc) + (c - a)/(ca))` `= x^((ca - bc + ab - ca + bc - ab)/(abc))` `= x^(0/(abc))` `= x^0` `= 1` `=`ডানপক্ষ `:. (x^a/x^b)^(1/(ab)) . (x^b/x^c)^(1/(bc)) . (x^c/x^a)^(1/(ca))` ` = 1` (প্রমাণিত)
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১৫.proman karo: `(x^a/x^b)^(1/(ab)) . (x^b/x^c)^(1/(bc)) . (x^c/x^a)^(1/(ca)) = 1`