Question

Which expression is equivalent to √4j^4/9k^8?

Answer 1

`( 2j^(2) )/( 3^(4) )`
SQRT each individual bit: 4 and
`j^(4)` and 9 and
`k^(8)`

Answer 2

Option (4) is correct.

An equivalent expression to the given expression
`\sqrt{(4j^4)/(9k^8)}` is
`(2j^2)/(3k^4)`

Explanation:

Given expression
`\sqrt{(4j^4)/(9k^8)}`

We have to choose an equivalent expression to the given expression
`\sqrt{(4j^4)/(9k^8)}`

Consider the given expression
`\sqrt{(4j^4)/(9k^8)}`

Apply radical rule,

`\sqrt[n]{(a)/(b)}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}`

`=(√(4)√(j^4))/(√(9)√(k^8))`

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:`

`√(4j^4)=√(4)√(j^4)`

`√(9k^8)=√(9)√(k^8)`

We have,

`=(√(4)√(j^4))/(√(9)√(k^8))`

`=(2√(j^4))/(3√(k^8))`

`\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{(m)/(n)}`

`=(2j^2)/(3k^4)`

Thus, An equivalent expression to the given expression
`\sqrt{(4j^4)/(9k^8)}` is
`(2j^2)/(3k^4)`