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Examveda

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

A. 1

B. 4

C. 6

D. 7

E. None of these

Answer: Option C

Solution(By Examveda Team)

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

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