[tex]\sqrt{m^4 n^7}\\ \\\\=\left( m^4 n^7 \right)^{\tfrac 12}~~~~~~~~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12}\right]\\\\\\=\left(m^4 \right)^{\tfrac 12} \cdot \left(n^7 \right)^{\tfrac 12} \\\\\\=m^{\tfrac 42} \cdot n^{\tfrac 72}\\\\\\=m^2 n^{\tfrac 72}[/tex]
