Question

In the given expression $(pr+q{)}^{(p-q)},p,q$ and $r$ can be any positive integer greater than 1 and less than 5. What is the largest possible value of the expression ?

• A. $64$
• B. $256$
• C. $324$
• D. Can't be determined
  

Answer 1

Answer: (C)

$324$

The expression $(pr+q{)}^{(p-q)}$ will have the maximum value, if the power is maximum which gives $p=4$ and $q=2$ such that

$p-q=4-2=2$

For maximum value, $r=4$

Therefore,

$pr+q=4\times 4+2=18$

Now, $(18{)}^2=324$