| Direction: What will come in place of the question mark (?) in the following question? |
A) 8
B) 6
C) 7
D) 10
E) None of these
Correct Answer: C
Solution :
\[{{4}^{6}}\times {{({{4}^{2}})}^{3}}\div {{4}^{2}}={{4}^{?}}\times {{4}^{3}}\] \[\Rightarrow \]\[{{4}^{6}}\times {{4}^{6}}\div {{4}^{2}}\div {{4}^{?}}\div {{4}^{3}}={{4}^{?}}\] \[\Rightarrow \]\[{{4}^{6+6-2-3}}={{4}^{?}}\] \[\Rightarrow \]\[{{4}^{7}}\Rightarrow {{4}^{?}}\Rightarrow ?=7\] Note:\[\begin{align} & [{{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \\ & {{a}^{m}}\div {{a}^{n}}={{a}^{m-n}} \\ & {{({{a}^{m}})}^{n}}={{a}^{mn}}] \\ \end{align}\]
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