To simplify the expression \(\left(\frac{1}{2z^2}\right) \left(\frac{25}{54}\right)\), follow these steps:

### Step 1: Multiply the numerators
\[
1 \times 25 = 25
\]

### Step 2: Multiply the denominators
\[
2z^2 \times 54 = 108z^2
\]

### Step 3: Combine the results
\[
\frac{25}{108z^2}
\]

So, the simplified expression is:
\[
\frac{25}{108z^2}
\]

Would you like a more detailed explanation or have any other questions?

### Related Questions:
1. How would the expression change if \( z \) had a specific value?
2. What if the numerator was \( \frac{1}{3z^3} \) instead of \( \frac{1}{2z^2} \)?
3. How can you apply this method to more complex algebraic fractions?
4. What happens if we divide \( \frac{25}{108z^2} \) by another fraction?
5. How does this simplify if \( z = 1 \)?

### Tip:
When multiplying fractions, always multiply the numerators and denominators separately, then simplify if possible.

Learn how to simplify the algebraic expression (1/2z²)(25/54) by multiplying the numerators and denominators separately. This detailed solution is suitable for students in Grades 6-8, covering key algebraic concepts like multiplying fractions and rational expressions.

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