If A = $$\frac{{\sqrt {0.0004} \times \root 3 \of {0.000008} }}{{\root 4 \of {16000} \times \root 3 \of {125000} \times \root 4 \of {810} }}$$      and B = $$\frac{{\root 3 \of {0.729} \times \root 4 \of {0.0016} }}{{\sqrt {0.16} }},$$    what is A × B?

Solution (By Examveda Team)

$$\eqalign{ & {\text{A}} = \frac{{\sqrt {0.0004} \times \root 3 \of {0.000008} }}{{\root 4 \of {16000} \times \root 3 \of {125000} \times \root 4 \of {810} }} \cr & = \frac{{0.02 \times 0.02}}{{\root 4 \of {16000 \times 810} \times \root 3 \of {125000} }} \cr & = \frac{{0.02 \times 0.02}}{{20 \times 3 \times 50}} \cr & = \frac{1}{{75 \times {{10}^5}}} \cr & {\text{B}} = \frac{{\root 3 \of {0.729} \times \root 4 \of {0.0016} }}{{\sqrt {0.16} }} \cr & = \frac{{0.9 \times 0.2}}{{0.4}} \cr & = \frac{9}{{20}} \cr & \therefore A \times B = \frac{1}{{75 \times {{10}^5}}} \times \frac{9}{{20}} \cr & = \frac{3}{{25 \times 2}} \times \frac{1}{{{{10}^6}}} \cr & = \frac{3}{5} \times \frac{1}{{{{10}^7}}} \cr & = \frac{3}{5} \times {10^{ - 7}} \cr & = 6 \times {10^{ - 8}} \cr} $$