${(6)}^{4} \div {(36)}^{3} \times 216 = 6^{(? - 5)}$ ${\left( 6 \right)^4} \div {\left( {36} \right)^3} \times 216 = {6^{\left( {? - 5} \right)}}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let , \\ {(6)}^{4} \div {(36)}^{3} \times 216 = 6^{(x - 5)} \\ Then, \\ 6^{(x - 5)} = {(6)}^{4} \div {(6^{2})}^{3} \times 6^{3} \\ \Rightarrow 6^{(x - 5)} = 6^{4} \div 6^{(2 \times 3)} \times 6^{3} \\ \Rightarrow 6^{(x - 5)} = 6^{4} \div 6^{6} \times 6^{3} \\ \Rightarrow 6^{(x - 5)} = 6^{(4 - 6 + 3)} \\ \Rightarrow 6^{(x - 5)} = 6 \\ \Rightarrow x - 5 = 1 \\ \Rightarrow x = 6 \end{aligned}

$\eqalign{ & {\text{Let ,}} \cr & {\left( 6 \right)^4} \div {\left( {36} \right)^3} \times 216 = {6^{\left( {x - 5} \right)}} \cr & {\text{Then,}} \cr & {6^{\left( {x - 5} \right)}} = {\left( 6 \right)^4} \div {\left( {{6^2}} \right)^3} \times {6^3} \cr & \Rightarrow {6^{\left( {x - 5} \right)}} = {6^4} \div {6^{\left( {2 \times 3} \right)}} \times {6^3} \cr & \Rightarrow {6^{\left( {x - 5} \right)}} = {6^4} \div {6^6} \times {6^3} \cr & \Rightarrow {6^{\left( {x - 5} \right)}} = {6^{\left( {4 - 6 + 3} \right)}} \cr & \Rightarrow {6^{\left( {x - 5} \right)}} = 6 \cr & \Rightarrow x - 5 = 1 \cr & \Rightarrow x = 6 \cr}$