Question

simplify the expression.
\\(\frac{-18j^{2}k^{3}}{2j^{-7}k}\\)

Explanation:

Step1: Simplify the coefficient

We divide the coefficient of the numerator by the coefficient of the denominator. So, $\frac{-18}{2} = -9$.

Step2: Simplify the variable \( j \)

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for the variable \( j \), we have $j^{2-(-7)} = j^{2 + 7}=j^{9}$.

Step3: Simplify the variable \( k \)

Using the same rule of exponents for the variable \( k \), we get $k^{3 - 1}=k^{2}$.

Step4: Combine the results

Multiply the simplified coefficient, the simplified \( j \) term, and the simplified \( k \) term together. So we have $-9\times j^{9}\times k^{2}=-9j^{9}k^{2}$.

Answer:

\(-9j^{9}k^{2}\)