One approach is to isolate the 3 in both equations. Here’s what I mean:

Given: \(3^k = 16\)
Rewrite \(16\) as \(2^4\) to get: \(3^k = 2^4\)
Raise both sides to the power of \(\frac{1}{k}\) to get: \((3^k)^{(\frac{1}{k})} = (2^4)^{(\frac{1}{k})}\)
Use power of power law to simplify: \(3 = 2^{(\frac{4}{k})}\)

Given: \(2^j = 27\)
Rewrite \(27\) as \(3^3\) to get: \(2^j = 3^3\)
Raise both sides to the power of \(\frac{1}{3}\) to get: \( (2^j)^{(\frac{1}{3})} = (3^3)^{(\frac{1}{3})}\)
Use power of power law to simplify: \(2^(\frac{j}{3}) = 3\)

We now have two equations:
\(3 = 2^{(\frac{4}{k})}\)
\(2^{(\frac{j}{3})} = 3\)

Since both equations are set equal to 3, we can write: \(2^{(\frac{4}{k})}\) \(=\) \(2^{(\frac{j}{3})}\)

Since the bases both equal 2, we can conclude that \(\frac{4}{k} = \frac{j}{3}\)
Cross multiply to get: \(jk = (4)(3) \)
So, \(jk = 12\)

Answer: D

Cheers,
Brent