Answer:
[tex] 20 i^{4} j^{2} k^{3}[/tex]
Step-by-step explanation:
We have to simplify the following expression:
[tex]\sqrt{400i^{8} j^{4} k^{6} }[/tex]
400 can be written as square of 20. The given expression can be simplified using the properties of exponents as shown below
[tex]\sqrt{20^{2} i^{8} j^{4} k^{6} }\\\\ =\sqrt{(20)^{2}(i^{4} )^{2} (j^{2} )^{2} (k^{3} )^{2} } \\\\=\sqrt{(20 i^{4} j^{2} k^{3} )^{2} } \\\\ =((20 i^{4} j^{2} k^{3} )^{2})^{\frac{1}{2} }\\\\ =20 i^{4} j^{2} k^{3}[/tex]
Properties used:
[tex]x^{m \times n}=(x^{m})^{n} \\\\\sqrt{x} =x^{\frac{1}{2} }[/tex]
