| The value of question mark (?) in \[{{(4\times 4\times 4\times 4\times 4\times 4)}^{5}}\times {{(4\times 4\times 4)}^{8}}\div \,\,{{(4)}^{3}}={{(64)}^{?}}\] is |
A) 17
B) 10
C) 16
D) 11
E) None of these
Correct Answer: A
Solution :
| \[{{(4\times 4\times 4\times 4\times 4\times 4)}^{5}}\times {{(4\times 4\times 4)}^{8}}\div {{(4)}^{3}}={{(64)}^{?}}\] |
| \[\Rightarrow \]\[{{({{4}^{6}})}^{5}}\times {{({{4}^{3}})}^{8}}\times \frac{1}{{{(4)}^{3}}}={{({{4}^{3}})}^{?}}\] |
| \[\Rightarrow \]\[{{(4)}^{30}}\times {{(4)}^{24}}\times \frac{1}{{{(4)}^{3}}}={{({{4}^{3}})}^{?}}\] |
| \[\Rightarrow \]\[{{(4)}^{30+24-3}}=({{4}^{3}})\]\[\Rightarrow \]\[{{(4)}^{51}}={{({{4}^{3}})}^{?}}\] |
| On comparing both sides, we get |
| \[3\times ?=51\]\[\Rightarrow \]\[?=\frac{51}{3}=17\] |
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