The mathematical expression in the image appears to be:

$\frac{\left( 8^{\frac{2}{3}} \cdot 92^{\frac{1}{92}} \right)}{32^{\frac{2}{5}} \cdot 27^{\frac{1}{3}}}$

Now, let's break it down and simplify it step by step:

Step 1: Simplify $8^{\frac{2}{3}}$

We know that $8 = 2^3$, so: $8^{\frac{2}{3}} = \left( 2^3 \right)^{\frac{2}{3}} = 2^2 = 4$

Step 2: Simplify $92^{\frac{1}{92}}$

Any number $x^{\frac{1}{x}}$ is very close to 1 as $x$ becomes large. So, for approximation purposes: $92^{\frac{1}{92}} \approx 1$

Step 3: Simplify $32^{\frac{2}{5}}$

We know that $32 = 2^5$, so: $32^{\frac{2}{5}} = \left( 2^5 \right)^{\frac{2}{5}} = 2^2 = 4$

Step 4: Simplify $27^{\frac{1}{3}}$

We know that $27 = 3^3$, so: $27^{\frac{1}{3}} = \left( 3^3 \right)^{\frac{1}{3}} = 3$

Step 5: Put it all together

Now, substitute the simplified values back into the original expression: $\frac{4 \cdot 1}{4 \cdot 3} = \frac{4}{12} = \frac{1}{3}$

So, the value of the expression is $\frac{1}{3}$.

Would you like more details or have any other questions?

Here are 5 related questions for further practice:

1. How would you simplify an expression like $16^{\frac{3}{4}}$?
2. Can you calculate $125^{\frac{2}{3}}$?
3. What is the approximate value of $93^{\frac{1}{93}}$?
4. Simplify the expression $64^{\frac{2}{6}} \cdot 49^{\frac{1}{2}}$.
5. How do we handle fractional exponents in the denominator?

Tip: When simplifying fractional exponents, try to express the base in terms of prime factors first—it often makes the calculations much easier!