A few important exponent rules:

(1) \((n^x)^y = n^{xy}\)

(2) \((n^x)/(n^y) = n^{x-y}\)

(3)\((n^x)(n^y) = n^{x+y}\)

(4) If \(n^x = n^y\), then \(x=y\)

Now, on to the problem:

The denominator on the left side can be simplified to \(b^{14}\).

\(\frac{b^{30}}{b^{14}} = b^{16}\).

Then, simplify the other term in the numerator to \(b^{4x}\).

Multiply that by \(b^{16}\) and we are left with \(b^{4x+16}\) on the left side of the equation.

The other side simplifies to \(b^{x+37}\). Since the bases are the same, using rule 4 we can create a new equation: 4x+16 < x+37. Solve for x and we we get x<7.

Since x is less than 7, Quantity B will always be greater than Quantity A. Thus the correct answer is B.