Answer:
Option (4) is correct.
An equivalent expression to the given expression [tex]\sqrt{\frac{4j^4}{9k^8}}[/tex] is [tex]\frac{2j^2}{3k^4}[/tex]
Step-by-step explanation:
Given expression [tex]\sqrt{\frac{4j^4}{9k^8}}[/tex]
We have to choose an equivalent expression to the given expression [tex]\sqrt{\frac{4j^4}{9k^8}}[/tex]
Consider the given expression [tex]\sqrt{\frac{4j^4}{9k^8}}[/tex]
Apply radical rule,
[tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]
[tex]=\frac{\sqrt{4}\sqrt{j^4}}{\sqrt{9}\sqrt{k^8}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:[/tex]
[tex]\sqrt{4j^4}=\sqrt{4}\sqrt{j^4}[/tex]
[tex]\sqrt{9k^8}=\sqrt{9}\sqrt{k^8}[/tex]
We have,
[tex]=\frac{\sqrt{4}\sqrt{j^4}}{\sqrt{9}\sqrt{k^8}}[/tex]
[tex]=\frac{2\sqrt{j^4}}{3\sqrt{k^8}}[/tex]
[tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
[tex]=\frac{2j^2}{3k^4}[/tex]
Thus, An equivalent expression to the given expression [tex]\sqrt{\frac{4j^4}{9k^8}}[/tex] is [tex]\frac{2j^2}{3k^4}[/tex]
