Directions for Questions 41 - 45: What value will come in place of the question mark (?) in the given questions?
${{7}^{2.3}}\times {{(7\times 7)}^{4.7}}\times {{(7\times 9)}^{3.4}}\times {{(9\times 9)}^{5.85}}={{63}^{?}}$
16.25
15.1
13.4
18.9
None of these
Solution
$\begin{align}
& {{63}^{?}}={{7}^{2.3}}\times {{(7\times 7)}^{4.7}}\times {{(7\times 9)}^{3.4}}\times {{(9\times 9)}^{5.85}} \\
& ={{7}^{2.3}}\times {{7}^{9.4}}\times {{7}^{3.4}}\times {{9}^{3.4}}\times {{9}^{11.70}} \\
& ={{7}^{15.1}}\times {{9}^{15.1}}={{(7\times 9)}^{15.1}} \\
& \Rightarrow {{63}^{?}}={{63}^{15.1}} \\
& \Rightarrow ?=15.1 \\
\end{align}$