This is a tough one. However, you should visualize the solution up-front before to get into unuseful calculations.

QA $(\sqrt{7}) ^ {2x}$ (multiply the exponents)

$\frac{(\sqrt{7})^{2x}}{(\sqrt{7})^{11}}$

For the root's properties, the root of 7 becomes $7^{\frac{2x}{2}}$ and the denominator is $7^{\frac{11}{2}}$.

From this $7^x$ and $7^{5.5}$

$\frac{7^x}{7^{5.5}}$ VS $\frac{7^x}{7^{11}}$

Everything boils down to compare the denominator of the two fractions $7^{11} > 7^{5.5}$ as a number.

However, we must consider the fraction $\frac{1}{7^{5.5}}$ which is > of $\frac{1}{7^{11}}$

Therefore, A must be bigger

Hope this helps.

Regards