Answer:
a) \(20i^4j^2k^3\)
Step-by-step explanation:
Given expression is,
\(\sqrt{400i^8j^4k^6}\)
\(=\sqrt{400(i^4)^2(j^2)^2(k^3)^2}\) ( \(a^{mn}=(a^m)^n\) )
\(=\sqrt{(20)^2(i^4)^2(j^2)^2(k^3)^2}\) ( \((20)^2 = 400\) )
\(=\sqrt{(20i^4j^2k^3)^2}\) ( \(a^m.b^m=(ab)^m\) )
\(=((20i^4j^2k^3)^2)^{\frac{1}{2}}\) ( \(\sqrt{a}=(a)^{\frac{1}{2}\) )
\(=(20i^4j^2k^3)^{2\times \frac{1}{2}}\)
\(=20i^4j^2k^3\)
Option a) is correct.
