Question

if (2/3)^3×(2/5)^5×(2/3)^5=(2/3)n-2 then find the value of n​

Answer 1

Given :-

$\sf \: (\frac{2}{3})^{3} \times ( \frac{2}{3})^{5} = ( \frac{2}{3})^{n - 2}$

To find :-

• value of n

solution :-

$:\implies\sf \: (\frac{2}{3})^{3} \times ( \frac{2}{3})^{5} = ( \frac{2}{3})^{n - 2} \\ \\ \\ \\ :\implies\sf \: ( \frac{2}{3})^{3 + 5} = ( \frac{2}{3})^{n - 2} \\ \\ \\ :\implies\sf \: 3 + 5 = n - 2 \\ \\ \\ :\implies\sf \therefore \: n \: = 9$

so therefore value of n is 9