what is the product?\n$\frac{5k}{6}cdot\frac{3}{2k^{3}}$\n$\frac{5}{4k^{2}}$\n$\frac{5k^{2}}{4}$\n$\frac{5k^{…

Explanation:

Step1: Multiply numerators and denominators

$\frac{5k}{6} \times \frac{3}{2k^{3}}=\frac{5k\times3}{6\times2k^{3}}$

Step2: Simplify the coefficient and variables

The coefficient $5k\times3 = 15k$ and $6\times2k^{3}=12k^{3}$. So we have $\frac{15k}{12k^{3}}$. Then simplify the fraction $\frac{15}{12}=\frac{5}{4}$ and use the rule of exponents $\frac{k}{k^{3}}=\frac{1}{k^{2}}$ (since $a^{m}\div a^{n}=a^{m - n}$, here $m = 1$ and $n = 3$). So $\frac{15k}{12k^{3}}=\frac{5}{4k^{2}}$

Answer:

$\frac{5}{4k^{2}}$