Answer:
[tex]4\sqrt{7}a^3[/tex]
Step-by-step explanation:
[tex]\sqrt{112a^6} \\\\\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\\\\=\sqrt{112}\sqrt{a^6}\\\\=4\sqrt{7}\sqrt{a^6}\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{bc}=\left(a^b\right)^c\\\\a^6=a^{3\times\:2}=\left(a^3\right)^2\\\\=4\sqrt{7}\sqrt{\left(a^3\right)^2}\\\\\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a\\\\\sqrt{\left(a^3\right)^2}=a^3\\\\=4\sqrt{7}a^3[/tex]
