https://file.aiquickdraw.com/mathbot/file/1728931386600bky5tdkx.jpg

The expression in the image reads:

\[
\frac{15ab}{36x^2y^2} \times \frac{24x^3y^2}{5(ab)^2}
\]

We can simplify it step by step.

### Step 1: Multiply the numerators and the denominators.
\[
\frac{15ab \times 24x^3y^2}{36x^2y^2 \times 5(ab)^2}
\]
This becomes:
\[
\frac{15 \times 24 \times ab \times x^3 \times y^2}{36 \times 5 \times x^2 \times y^2 \times (ab)^2}
\]

### Step 2: Simplify the constants.
\[
15 \times 24 = 360 \quad \text{and} \quad 36 \times 5 = 180
\]
Thus, the fraction becomes:
\[
\frac{360abx^3y^2}{180x^2y^2(ab)^2}
\]
Simplify the constant fraction:
\[
\frac{360}{180} = 2
\]
So, now we have:
\[
2 \times \frac{abx^3y^2}{x^2y^2(ab)^2}
\]

### Step 3: Simplify the variables.
- For \(x^3 / x^2\), we subtract the exponents: \(x^{3-2} = x^1 = x\).
- For \(y^2 / y^2\), the \(y^2\) cancels out.
- For \(ab / (ab)^2\), which is \(ab / ab^2 = 1 / ab\).

Thus, the expression simplifies to:
\[
2 \times \frac{x}{ab}
\]

### Final Answer:
\[
\frac{2x}{ab}
\]

Would you like more details or have any questions?

Here are five related questions:
1. How do you multiply fractions with variables and constants?
2. How do you simplify powers of variables when dividing?
3. What happens to terms that cancel out in a fraction?
4. Why do we subtract exponents when dividing powers of the same base?
5. Can we simplify the expression further if additional information about the variables is given?

**Tip:** Always simplify constants and variables separately for clarity when simplifying complex algebraic expressions.

Simplify the expression: (15ab / 36x^2y^2) * (24x^3y^2 / 5(ab)^2)

Learn how to simplify the algebraic expression (15ab / 36x^2y^2) * (24x^3y^2 / 5(ab)^2) using multiplication of fractions and exponent rules. Step-by-step solution included. Suitable for students in Grades 8-10.

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