Question

${\displaystyle {\left(\frac{6}{13}\right)}^{10}÷{\left[{\left(\frac{6}{13}\right)}^5\right]}^2={\left(\frac{6}{13}\right)}^{-}}$

Answer 1

${\displaystyle {\left(\frac{6}{13}\right)}^{10}÷{\left[{\left(\frac{6}{13}\right)}^5\right]}^2={\left(\frac{6}{13}\right)}^{\underline{0}}}$

Explanation:

Here, ${\displaystyle {\left(\frac{6}{10}\right)}^{10}÷{\left[{\left(\frac{6}{13}\right)}^5\right]}^2={\left(\frac{6}{13}\right)}^{10}÷{\left(\frac{6}{13}\right)}^{5\times 2}}$  ......[∵ (a^m)ⁿ = a^mn]

= ${\displaystyle {\left(\frac{6}{13}\right)}^{10}÷{\left(\frac{6}{13}\right)}^{10}={\left(\frac{6}{13}\right)}^{10-10}}$ ......[∵ a^m ÷ aⁿ = a^m–n, (m > n)]

= ${\displaystyle {\left(\frac{6}{13}\right)}^0}$

∴ ${\displaystyle {\left(\frac{6}{13}\right)}^{10}÷{\left[{\left(\frac{6}{13}\right)}^5\right]}^2={\left(\frac{6}{13}\right)}^0}$