Question

Determinati nr natural n din egalitatea: [( 3/5)^6]^10 = [(9/25)^5]^n
Cu explicatie!!

Answer 1

   
[tex]\displaystyle\\ \left[\left(\frac{3}{5}\right)^6\right]^{10}=\left\{\left[\frac{9}{25}\right]^5 \right\}^n\\ \left[\left(\frac{3}{5}\right)^6\right]^{10}=\left\{\left[\frac{3^2}{5^2}\right]^5 \right\}^n\\ \left[\left(\frac{3}{5}\right)^6\right]^{10}=\left\{\left[\left(\frac{3}{5}\right)^2 \right]^5 \right\}^n\\ \left(\frac{3}{5}\right)^{6\times10}=\left(\frac{3}{5}\right)^{2\times5\times n} \\ \left(\frac{3}{5}\right)^{60}=\left(\frac{3}{5}\right)^{10n}\\\\ 10n=60\\ n=\frac{60}{10}\\ \boxed{\bf n=6}[/tex]