Question

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

Explanation:

Step1: Simplify the coefficients and variables

First, handle the coefficients: $\frac{2}{3}$ divided by $-4$ is $\frac{2}{3} \times \frac{1}{-4} = \frac{2}{-12} = -\frac{1}{6}$. Then, for the variables with exponents, we have $x^{3/2}$ divided by $x$ (which is $x^1$). Using the rule of exponents $a^m \div a^n = a^{m - n}$, we get $x^{3/2 - 1} = x^{1/2}$.

Step2: Combine the results

Multiply the coefficient and the variable part together: $-\frac{1}{6} \times x^{1/2} = -\frac{x^{1/2}}{6}$ or $-\frac{\sqrt{x}}{6}$.

Answer:

$-\frac{\sqrt{x}}{6}$ (or $-\frac{x^{\frac{1}{2}}}{6}$)