### Multiplying Rational ExpressionsTo multiply rational expressions, we use the rule for multiplying rational expressions by factoring the numerators and denominators to remove any common factors. Here’s a detailed example to demonstrate this process.#### Example: Multiply \[ \frac{25a^3}{11b} \cdot \frac{b}{5a} \]To find the product, we use the following steps:1. **Multiplying the Numerators and Denominators:** \[ \frac{25a^3}{11b} \cdot \frac{b}{5a} = \frac{25a^3 \cdot b}{11b \cdot 5a} \]2. **Factoring Common Factors:** It is apparent that both the numerator and denominator have common factors such as 5, \(a\), and \(b\). Breaking them down: \[ \frac{25a^3 \cdot b}{11b \cdot 5a} = \frac{5 \cdot 5 \cdot a \cdot a \cdot a \cdot b}{11 \cdot b \cdot 5 \cdot a} \]3. **Simplifying the Expression:** Next, we simplify by replacing common factors: \[ \frac{5 \cdot 5 \cdot a \cdot a \cdot a \cdot b}{11 \cdot b \cdot 5 \cdot a} = \frac{1 \cdot 5 \cdot 1 \cdot a \cdot a \cdot 1}{11 \cdot 1 \cdot 1 \cdot a} \] \[ 5 = \frac{5a^2}{11} \]4. **Final Result:** \[ \frac{5a^2}{11} \]Thus, the simplified form of the product is: \[ \frac{5a^2}{11} \]### Practice Problem: Multiply\[ \frac{x^{11}}{10y} \cdot \frac{15y}{11x^7} \]Follow the same steps as above to simplify the expression.---### Explanation of the Provided Content:- **Title and Introduction:** The expression starts with explaining the goal and process of multiplying

Name: ### Multiplying Rational ExpressionsTo multiply rational expressions,
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: ### Multiplying Rational ExpressionsTo multiply rational expressions, we use the rule for multiplying rational expressions by factoring the numerators and denominators to remove any common factors. Here’s a detailed example to demonstrate this proce