Answer:
[tex]\sqrt[15]{x^7}[/tex]
Step-by-step explanation:
If we have the expression
[tex]\frac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}[/tex], we have to think about exponent rules.
If we have [tex]a^b \div a^c[/tex], then the value will be equal to [tex]a^{b-c}[/tex].
So [tex]\frac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}[/tex] simplified will be [tex]x^{\frac{4}{5} - \frac{1}{3}}[/tex]
Converting [tex]\frac{4}{5}[/tex] and [tex]\frac{1}{3}[/tex] into fifteenths (lcm) gets us [tex]\frac{12}{15} - \frac{5}{15} = \frac{7}{15}[/tex].
We can convert [tex]x^{\frac{7}{15}}[/tex] into a radical by taking the denominator root of x to the numerator.
[tex]\sqrt[15]{x^7}[/tex].
Hope this helped!
