Question

evaluate the left hand side to find the value of $a$ in the equation in simplest form.
$\frac{x^{\frac{1}{3}}}{x}=x^{a}$

Explanation:

Step1: Rewrite denominator as exponent

$x = x^1$

Step2: Apply exponent subtraction rule

When dividing like bases, subtract exponents: $\frac{x^m}{x^n}=x^{m-n}$. Here $m=\frac{1}{3}$, $n=1$.
$x^{\frac{1}{3}-1}$

Step3: Simplify the exponent

$\frac{1}{3}-1 = \frac{1}{3}-\frac{3}{3}=-\frac{2}{3}$

Answer:

$-\frac{2}{3}$