| Directions: What will come in place of the question mark (?) in the following questions? |
| \[{{(4\times 4)}^{3}}\div {{(512\div 8)}^{4}}\times {{(32\times 8)}^{4}}={{(2\times 2)}^{?+4}}\] |
A) 8
B) 12
C) 6
D) 14
Correct Answer: C
Solution :
| \[\frac{{{(4\times 4)}^{3}}}{{{\left( \frac{512}{8} \right)}^{4}}}\times {{(32\times 8)}^{4}}={{(2\times 2)}^{?+4}}\] |
| \[\Rightarrow \]\[\frac{{{(16)}^{3}}}{{{(64)}^{4}}}\times {{(32\times 8)}^{4}}={{(4)}^{?+4}}\] |
| \[\Rightarrow \] \[\frac{{{4}^{6}}}{{{4}^{12}}}\times {{4}^{16}}={{(4)}^{?+4}}\] |
| \[\Rightarrow \] \[{{4}^{10}}={{4}^{?+4}}\]\[\Rightarrow \]\[?=6\] |
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