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 |
\[3\times ?=51\]\[\Rightarrow \]\[?=\frac{51}{3}=17\] |
You need to login to perform this action.
You will be redirected in
3 sec