Question

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

Answer 1

Solution

Given the expression below

$\frac{x^{\frac{5}{3}}}{x}=x^a$

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

$\frac{x^m}{x^n}=x^{m-n}$

Applyin it to the expression gives

$\begin{gathered} \frac{x^{\frac{5}{3}}}{x}=x^a \\ x^{\frac{5}{3}-1}=x^a \\ x^{\frac{5-3}{3}}=x^a \\ x^{\frac{2}{3}}=x^a \end{gathered}$

Simplifying to find a

$\begin{gathered} x^{\frac{2}{3}}=x^a \\ \frac{2}{3}=a \\ a=\frac{2}{3} \end{gathered}$

Hence, the value of a is 2/3