It looks like you are dealing with a multiplication of algebraic expressions:

\[
\frac{14a^2b^4}{21x^5y^2} \times \frac{35x^3y}{16ab}
\]

We can simplify this step by step.

### Step 1: Write the expression clearly
\[
\frac{14a^2b^4}{21x^5y^2} \times \frac{35x^3y}{16ab}
\]

### Step 2: Multiply the numerators and the denominators
Multiply the two fractions by multiplying the numerators and the denominators:

Numerator: \(14a^2b^4 \times 35x^3y = 14 \times 35 \times a^2 \times b^4 \times x^3 \times y\)

Denominator: \(21x^5y^2 \times 16ab = 21 \times 16 \times x^5 \times y^2 \times a \times b\)

### Step 3: Perform the multiplications
Numerator: \(14 \times 35 = 490\)

Denominator: \(21 \times 16 = 336\)

Thus, we have:

\[
\frac{490a^2b^4x^3y}{336x^5y^2ab}
\]

### Step 4: Simplify coefficients
\[
\frac{490}{336} = \frac{35}{24}
\]

### Step 5: Simplify the variables
- For \(a^2\) and \(a\), we simplify as \(a^2/a = a\)
- For \(b^4\) and \(b\), we simplify as \(b^4/b = b^3\)
- For \(x^3\) and \(x^5\), we simplify as \(x^3/x^5 = \frac{1}{x^2}\)
- For \(y\) and \(y^2\), we simplify as \(y/y^2 = \frac{1}{y}\)

### Step 6: Write the simplified result
\[
\frac{35ab^3}{24x^2y}
\]

So, the simplified expression is:

\[
\frac{35ab^3}{24x^2y}
\]

Would you like further clarification or additional details on any step?

Here are five related questions:
1. How do you simplify powers of variables when dividing?
2. Can you explain how to multiply algebraic fractions?
3. How do you simplify coefficients when multiplying fractions?
4. What are the rules for simplifying exponents in a fraction?
5. How would the result change if the exponents were different?

**Tip:** When simplifying fractions, always reduce both the numerical coefficients and the variables with exponents separately.

Learn how to simplify the algebraic expression (14a²b⁴ / 21x⁵y²) × (35x³y / 16ab) step-by-step. This problem covers multiplication of algebraic fractions, exponent rules, and simplification techniques. Ideal for students in Grades 9-11 looking to deepen their understanding of algebra.

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