Given:
There are given the equation:
[tex]\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}=x^a[/tex]Explanation:
To find the value of a, first, we need to apply the exponent rule:
So,
From the exponent rule:
[tex]\frac{x^p}{x^q}=x^{p-q}[/tex]Then,
Apply the above rule to the given question:
So,
[tex]\begin{gathered} \frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}}}=x^a \\ x^{\frac{4}{3}-\frac{2}{3}}=x^a \end{gathered}[/tex]Now,
From the second rule of the exponent:
[tex]\begin{gathered} x^{p-q}=x^d \\ p-q=d \end{gathered}[/tex]Then,
Apply above second rule into the given equation:
[tex]\begin{gathered} x^{\frac{4}{3}-\frac{2}{3}}=x^a \\ \frac{4}{3}-\frac{2}{3}=a \end{gathered}[/tex]Then,
[tex]\begin{gathered} \frac{4}{3}-\frac{2}{3}=a \\ \frac{4-2}{3}=a \\ \frac{2}{3}=a \end{gathered}[/tex]Final answer:
Hence, the value of the a is shown below:
[tex]a=\frac{2}{3}[/tex]