Answer:
Simplest form is [tex]a^{\frac{2}{15} }[/tex].
Step-by-step explanation:
Given : [tex]\frac{\sqrt[5]{a^{4}}}{\sqrt[3]{a^{2}}}[/tex].
To find : Which of the following is the simplest form of this expression?
Solution: We have given :
[tex]\frac{\sqrt[5]{a^{4}}}{\sqrt[3]{a^{2}}}[/tex]
By the radical rule [tex]\sqrt[a]{b^{c} } = b^{\frac{c}{a}}[/tex],
Then
[tex]\frac{\sqrt[5]{a^{4}}}{\sqrt[3]{a^{2}}}[/tex] = [tex]\frac{a^{\frac{4}{5}}}{a^{\frac{2}{3}}}[/tex].
⇒[tex]a^{\frac{4}{5} -\frac{2}{3}}[/tex].
⇒ [tex]a^{\frac{12-10}{15} }[/tex].
⇒ [tex]a^{\frac{2}{15} }[/tex].
Therefore, Simplest form is [tex]a^{\frac{2}{15} }[/tex].
