#### Answer

$160m^{2}p\sqrt {7n}$

#### Work Step by Step

Step 1: $8m\sqrt {14mn}\times2p\sqrt {50m}$
Step 2: $8m\times2p\times\sqrt {14mn}\times\sqrt {50m}$
Step 3: $16mp\times\sqrt {14mn\times50m}$
Step 4: $16mp\times\sqrt {700m^{2}n}$
Step 4: $16mp\times\sqrt {7\times100\times m^{2}\times n}$
Step 5: $16mp\times10m\sqrt {7n}$
Step 6: $160m^{2}p\sqrt {7n}$