#### Answer

$\color{blue}{-30m^5n^3p\sqrt{6mp}}$

#### Work Step by Step

Simplify each radical:
$=4m^3\sqrt{25m^4n^6p^2(6mp)}-5n^2\sqrt{100m^{10}n^2p^2(6mp)}
\\=4m^3\sqrt{5^2(m^2)^2(n^3)^2p^2(6mp)}-5n^2\sqrt{10^2(m^5)^2n^2p^2(6mp)}
\\=4m^3(5m^2n^3p)\sqrt{6mmp} - 5n^2(10m^5np)\sqrt{6mp}
\\=20m^5n^3p\sqrt{6mp} - 50m^5n^3p\sqrt{6mp}$
Combine like terms to obtain:
$=(20-50)m^5n^3p\sqrt{6mp}
\\=\color{blue}{-30m^5n^3p\sqrt{6mp}}$