https://file.aiquickdraw.com/mathbot/file/1725997906076z8yt8ken.jpg

In the image, you are asked to order expressions using the symbols `>`, `<`, or `=`.

The expressions shown are:

1. \( \frac{2^2 \times 4^2}{2} \) 
2. \( \frac{2^4 \times 2^2}{4} \)
3. \( \frac{4^2}{2 \times 8} \)

### Let’s simplify each expression:

1. \( \frac{2^2 \times 4^2}{2} = \frac{4 \times 16}{2} = \frac{64}{2} = 32 \)

2. \( \frac{2^4 \times 2^2}{4} = \frac{16 \times 4}{4} = \frac{64}{4} = 16 \)

3. \( \frac{4^2}{2 \times 8} = \frac{16}{16} = 1 \)

### Now we compare:

- \( 32 > 16 > 1 \)

So the correct order is:

\[ \frac{2^2 \times 4^2}{2} > \frac{2^4 \times 2^2}{4} > \frac{4^2}{2 \times 8} \]

Would you like more details on how the simplifications were done or do you have any questions?

Here are five related questions for practice:

1. Simplify \( \frac{2^3 \times 4^2}{8} \).
2. Compare \( \frac{3^2 \times 5}{2^3} \) with \( \frac{3 \times 10}{4} \).
3. Find the value of \( \frac{5^3}{5^2 \times 5} \).
4. What is \( \frac{4^3}{2^2 \times 8} \) equal to?
5. Which is greater: \( \frac{2^5}{2^2 \times 4} \) or \( \frac{2^4 \times 2}{8} \)?

**Tip**: Always simplify powers and products before dividing for quicker comparisons!

Order the expressions: (2^2 * 4^2) / 2, (2^4 * 2^2) / 4, (4^2) / (2 * 8)

Learn how to order expressions involving exponents, multiplication, and division by simplifying each one. The expressions include powers of 2 and 4, and this problem helps in understanding exponent properties and comparison of values.

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