Simplify the expression sqrt(32²⁾27sqrt(3)

The image contains two distinct mathematical problems.

: Simplify the expression
The expression to simplify is $\frac{\sqrt{3^{2^{\sqrt{2}}}}}{27^{\sqrt{3}}}$.

Step 1: Rewrite the denominator with base 3.
We know that $27 = 3^3$.

$$27^{\sqrt{3}} = (3^3)^{\sqrt{3}} = 3^{3\sqrt{3}}$$

Step 2: Rewrite the numerator using fractional exponents.
The square root can be expressed as a power of $\frac{1}{2}$.

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