$$ \frac{\placeholder{}}{\placeholder{}} $$$$ \frac{2a^2}{3b}\cdot\frac{6b^2}{4a} $$

Let's simplify the expression step by step:

Given:
\[
\frac{2a^2}{3b} \cdot \frac{6b^2}{4a}
\]

### Step 1: Multiply the numerators and denominators
When multiplying fractions, you multiply the numerators together and the denominators together.

\[
\frac{2a^2 \cdot 6b^2}{3b \cdot 4a}
\]

### Step 2: Multiply the terms
In the numerator:
\[
2a^2 \cdot 6b^2 = 12a^2b^2
\]
In the denominator:
\[
3b \cdot 4a = 12ab
\]

So the expression becomes:
\[
\frac{12a^2b^2}{12ab}
\]

### Step 3: Simplify the fraction
Now, cancel out common factors from the numerator and denominator. First, cancel out the 12 from both the numerator and denominator:
\[
\frac{a^2b^2}{ab}
\]

Next, simplify the powers of $a$ and $b$:
\[
\frac{a^2}{a} = a \quad \text{and} \quad \frac{b^2}{b} = b
\]

So, the simplified result is:
\[
ab
\]

Thus, the simplified expression is:
\[
ab
\]

Do you have any questions or want more details on any step?

Here are five related questions:
1. How do you multiply more complex fractions with different powers?
2. What happens if there are negative exponents in the fraction?
3. How would you handle division instead of multiplication of fractions?
4. How does this simplify if $a$ or $b$ is zero?
5. How do you handle variables in the denominator when simplifying?

**Tip:** Always check for common factors between the numerator and denominator before multiplying or simplifying.

$$ \frac{2a^2}{3b} \cdot \frac{6b^2}{4a} $$

Learn how to simplify the algebraic fraction multiplication $$ \frac{2a^2}{3b} \cdot \frac{6b^2}{4a} $$ with detailed step-by-step instructions. This problem covers key algebraic concepts like fraction multiplication and exponent rules. Ideal for students in Grades 8-10.

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