Question

Which expression is equivalent to √400i^8j^4k^6?

a)20i^4j^2|k^3|

b)20i^6j^2k^4

c)200i^4j^2|k^3|

d)200i^6j^2k^4

Answer 1

`√(400i^8j^4k^6)=√(400)\cdot√(i^8)\cdot√(j^4)\cdot√(k^6)=20i^4j^2|k^3|\to\boxed{A.}`

Answer 2

a)
`20i^4j^2k^3`

Explanation:

Given expression is,

`√(400i^8j^4k^6)`

`=√(400(i^4)^2(j^2)^2(k^3)^2)` (
`a^(mn)=(a^m)^n` )

`=√((20)^2(i^4)^2(j^2)^2(k^3)^2)` (
`(20)^2 = 400` )

`=√((20i^4j^2k^3)^2)` (
`a^m.b^m=(ab)^m` )

`=((20i^4j^2k^3)^2)^{(1)/(2)}` (
`√(a)=(a)^{(1)/(2)` )

`=(20i^4j^2k^3)^{2* (1)/(2)}`

`=20i^4j^2k^3`

Option a) is correct.