Question

Evaluate the left hand side to find the value of aa in the equation in simplest form. 6

Answer 1

Given the expression below

`\frac{x^{(5)/(3)}}{x}=x^a`

To find the value of a, we apply the exponent rule, which is

`(x^m)/(x^n)=x^(m-n)`

Applyin it to the expression gives

`\begin{gathered} \frac{x^{(5)/(3)}}{x}=x^a \\ x^{(5)/(3)-1}=x^a \\ x^{(5-3)/(3)}=x^a \\ x^{(2)/(3)}=x^a \end{gathered}`

Simplifying to find a

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

Hence, the value of a is 2/3