Simplification Ques 11
Question-
$(4 \times 4)^{3} \div(512 \div 8)^{4} \times(32 \times 8)^{4}$ $=(2 \times 2)^{?+4}$
(1) 8
(2) 12
(3) 6
(4) 14
(5) None of these
Show Answer
Correct Answer: (3)
Solution: (3)
$\left(4^{2}\right)^{3} \div\left(\frac{512}{8}\right)^{4}$ $\times(4 \times 4 \times 2 \times 2 \times 4)^{4}=(4)^{?+4}$
$\Rightarrow 4^{6} \div\left(4^{3}\right)^{4} \times\left(4^{4}\right)^{4}=4^{?+4}$
$\left[a^{m} \times a^{n}=a^{m+n} ; a^{m} \div a^{n}=a^{m-n}\right]$
$\Rightarrow 4^{6} \div 4^{12} \times 4^{16}=4^{?+4}$
$\Rightarrow 4^{6-12+16}=4^{?+4}$
$\Rightarrow 4^{10}=4^{?+4} $
$\Rightarrow$ ? $+4=10$
$\Rightarrow$ ? $=10-4=6$
BETA
