Question

select the correct answer. which expression is equivalent to the given expression? assume the denominator does not equal zero. $\frac{8j^{4}k^{8}}{2j^{5}k^{6}}$ $\frac{4k^{2}}{j}$ $\frac{4k^{14}}{j^{9}}$ $4j^{-9}k^{14}$ $\frac{4}{j k^{2}}$

Explanation:

Step1: Divide the coefficients

Divide 8 by 2: $\frac{8}{2}=4$

Step2: Apply exponent - subtraction rule for $j$ terms

For $j$ terms, use the rule $\frac{a^m}{a^n}=a^{m - n}$. Here, $m = 4$ and $n = 5$, so $\frac{j^4}{j^5}=j^{4 - 5}=j^{-1}=\frac{1}{j}$

Step3: Apply exponent - subtraction rule for $k$ terms

For $k$ terms, $m = 8$ and $n=- 6$, so $\frac{k^8}{k^{-6}}=k^{8-(-6)}=k^{8 + 6}=k^{14}$

Step4: Combine the results

Combine the results from steps 1 - 3: $4\times\frac{1}{j}\times k^{14}=\frac{4k^{14}}{j}$

Answer:

$\frac{4k^{14}}{j}$ (assuming the first option in the list you provided is $\frac{4k^{14}}{j}$ as the formatting of the options is a bit unclear in the image. If the first option is actually $\frac{4k^{2}}{j}$, then the above - shown steps are for the general process of simplifying the given rational expression)