We need to simplify the given expression:
[tex]\frac{a^{\frac{1}{3}}\cdot a^{\frac{5}{3}}}{a^{-\frac{4}{3}}}[/tex]We can rewrite the expression like this:
[tex]\frac{a^{\frac{1}{3}}}{a^{-\frac{4}{3}}}\cdot a^{\frac{5}{3}}[/tex]Now, use the next property for negative exponents:
[tex]\frac{1}{a^{-n}}=a^n[/tex]Then:
[tex]a^{\frac{1}{3}}\cdot a^{\frac{4}{3}}\cdot a^{\frac{5}{3}}[/tex]If we have exponents with the same base, we can sum the exponents:
Therefore:
[tex]a^{\frac{1}{3}+\frac{4}{3}+\frac{5}{3}}=a^{\frac{10}{3}}[/tex]