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

$\sqrt{400i^8j^4k^6}=\sqrt{400}\cdot\sqrt{i^8}\cdot\sqrt{j^4}\cdot\sqrt{k^6}=20i^4j^2|k^3|\to\boxed{A.}$

Answer 2

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.