3. simplify: $\frac{-6j^{3}k^{2}}{(-2j^{2}k^{3})^{2}}$

Explanation:

Step1: Expand numerator

$(-2j^{2}k^{3})^{2}=(-2)^{2}(j^{2})^{2}(k^{3})^{2}=4j^{4}k^{6}$

Step2: Rewrite the fraction

$\frac{4j^{4}k^{6}}{- 6j^{3}k^{2}}$

Step3: Simplify coefficients and variables

Coefficient: $\frac{4}{-6}=-\frac{2}{3}$. For variables with the same base, use the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$. So $\frac{j^{4}}{j^{3}}=j^{4 - 3}=j$ and $\frac{k^{6}}{k^{2}}=k^{6 - 2}=k^{4}$. The simplified form is $-\frac{2}{3}jk^{4}$

Answer:

$-\frac{2}{3}jk^{4}$