### Division of Algebraic Expressions**Problem Statement:**"Perform the division. See Example 2."The expression given for division is:\[ \frac{12(r^2s2)^2}{-3(rs^4)^3} \]**Steps to Solve:**1. **Simplify the Numerator:** - Distribute the exponent 2 across \( r^2 \) and \( s2 \): \[ (r^2s2)^2 = (r^2)^2(s2)^2 = r^{4}(2s)^2 = r^4 \cdot 4s^2 = 4r^4s^2 \] - Multiply by 12: \[ 12 \times 4r^4s^2 = 48r^4s^2 \]2. **Simplify the Denominator:** - Distribute the exponent 3 across \( rs^4 \): \[ (rs^4)^3 = r^3(s^4)^3 = r^3s^{12} \] - Multiply by -3: \[ -3 \times r^3s^{12} = -3r^3s^{12} \]3. **Combine and Simplify the Division:** - Write the simplified numerator and denominator: \[ \frac{48r^4s^2}{-3r^3s^{12}} \] - Factor and reduce the coefficients: \[ \frac{48}{-3} = -16 \] - Reduce the exponents using \( a^m / a^n = a^{m-n} \): \[ \frac{r^4}{r^3} = r^{4-3} = r \] \[ \frac{s^2}{s^{12}} = s^{2-12} = s^{-10} = \frac{1}{s^{10}} \] - Combine all parts: \[ -16 \times r \times \frac{1}{s^{10}} = -\frac{16r}{s^{10}} \]**Final Answer:**\[ -\frac{16r}{s^{10}} \]

Name: ### Division of Algebraic Expressions**Problem Statement:**"Perform t
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: ### Division of Algebraic Expressions**Problem Statement:**"Perform the division. See Example 2."The expression given for division is:\[ \frac{12(r^2s2)^2}{-3(rs^4)^3} \]**Steps to Solve:**1. **Simplify the Numerator:** - Distribute the exponen