Question

simplify the expression: \\(dfrac{x^{\frac{5}{6}}}{x^{\frac{1}{2}}}\\)

Explanation:

Step1: Simplify the coefficient

The coefficient is $\frac{\frac{5}{6}}{\frac{1}{2}}$. Dividing by a fraction is multiplying by its reciprocal, so $\frac{5}{6} \times 2 = \frac{5}{3}$.

Step2: Simplify the variable part

For the variable $x$, we use the rule of exponents $\frac{x^m}{x^n}=x^{m - n}$. Here, $m=\frac{5}{6}$ and $n = \frac{1}{2}=\frac{3}{6}$. So $x^{\frac{5}{6}-\frac{3}{6}}=x^{\frac{2}{6}}=x^{\frac{1}{3}}$.

Step3: Combine coefficient and variable

Multiply the coefficient and the variable part: $\frac{5}{3}x^{\frac{1}{3}}$.

Answer:

$\frac{5}{3}x^{\frac{1}{3}}$