Solution
Given the expression below
[tex]\frac{x^{\frac{5}{3}}}{x}=x^a[/tex]
To find the value of a, we apply the exponent rule, which is
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex]
Applyin it to the expression gives
[tex]\begin{gathered} \frac{x^{\frac{5}{3}}}{x}=x^a \\ x^{\frac{5}{3}-1}=x^a \\ x^{\frac{5-3}{3}}=x^a \\ x^{\frac{2}{3}}=x^a \end{gathered}[/tex]
Simplifying to find a
[tex]\begin{gathered} x^{\frac{2}{3}}=x^a \\ \frac{2}{3}=a \\ a=\frac{2}{3} \end{gathered}[/tex]
Hence, the value of a is 2/3
