Question

(36)^1/2 -(36)^9/2)/(36)^5/2 find the value of.

Answer 1

Dear Student,

$$\begin{gathered} \frac{{36}^{{\displaystyle \frac{1}{2}}}-{36}^{{\displaystyle \frac{9}{2}}}}{{36}^{{\displaystyle \raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}} \\ =\frac{6^{2\times {\displaystyle \frac{1}{2}}}-6^{2\times {\displaystyle \frac{9}{2}}}}{6^{2\times {\displaystyle \frac{5}{2}}}} \\ =\frac{6-6^9}{6^5} \\ =\frac{6\left(1-6^8\right)}{6^5} \\ =\frac{{\displaystyle \left(1-6^8\right)}}{{\displaystyle 6^4}} \\ =\frac{1}{6^4}-\frac{6^8}{6^4} \\ =\frac{1}{6^4}-6^4 \\ ={\left(\frac{1}{6^2}\right)}^2-{\left(6^2\right)}^2 \\ =\left(\frac{\mathbf{1}}{{\mathbf{6}}^{\mathbf{2}}}\mathbf{-}{\mathbf{6}}^{\mathbf{2}}\right)\left(\frac{\mathbf{1}}{{\mathbf{6}}^{\mathbf{2}}}\mathbf{+}{\mathbf{6}}^{\mathbf{2}}\right)\left[\left(a^2-b^2\right)=\left(a+b\right)\left(a-b\right)\right] \end{gathered}$$

Regards