Evaluate sqrt(63⁴).

We use the property that $\sqrt{x^n} = x^{n/2}$.

$$\sqrt{63^4} = 63^{\frac{4}{2}}$$ $$= 63^2$$

$$63^2 = 63 \times 63 = 3969$$

The evaluated expression is:

$$\boxed{\text{3969}}$$

We can separate the square root into the numerator and the denominator:

$$\sqrt{\frac{297}{64}} = \frac{\sqrt{297}}{\sqrt{64}}$$

Find the prime factors of 297:

$$297 = 3 \times 99 = 3 \times 9 \times 11 = 3 \times 3^2 \times 11$$

Now, take the square root:

$$\sqrt{297} = \sqrt{3^2 \times 3 \times 11} = \sqrt{3^2} \times \sqrt{3 \times 11} = 3\sqrt{33}$$

$$\frac{\sqrt{297}}{\sqrt{64}} = \frac{3\sqrt{33}}{8}$$

The simplified expression is:

$$\boxed{\frac{3\sqrt{33}}{8}}$$