https://file.aiquickdraw.com/mathbot/file/17271558428422xcj4mvn.jpg

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!

Nilai dari (8^(2/3) * 92^(1/92)) / (32^(2/5) * 27^(1/3)) adalah ...

Learn how to simplify the expression (8^(2/3) * 92^(1/92)) / (32^(2/5) * 27^(1/3)). This problem covers concepts of exponents, roots, and exponent rules for students in Grades 9-12.

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