Question

Evaluate the left hand side to find the value of a in the equation in simplest form. 8

Answer 1

Given:

There are given the equation:

`\frac{x^{(4)/(3)}}{x^{(2)/(3)}}=x^a`

Step-by-step explanation:

To find the value of a, first, we need to apply the exponent rule:

So,

From the exponent rule:

`(x^p)/(x^q)=x^(p-q)`

Then,

Apply the above rule to the given question:

So,

`\begin{gathered} \frac{x^{(4)/(3)}}{x^{(2)/(3)}}=x^a \\ x^{(4)/(3)-(2)/(3)}=x^a \end{gathered}`

Now,

From the second rule of the exponent:

`\begin{gathered} x^(p-q)=x^d \\ p-q=d \end{gathered}`

Then,

Apply above second rule into the given equation:

`\begin{gathered} x^{(4)/(3)-(2)/(3)}=x^a \\ (4)/(3)-(2)/(3)=a \end{gathered}`

Then,

`\begin{gathered} (4)/(3)-(2)/(3)=a \\ (4-2)/(3)=a \\ (2)/(3)=a \end{gathered}`

Final answer:

Hence, the value of the a is shown below:

`a=(2)/(3)`