4. $$ \frac{5 x^{-2} y(3 x y)^{2}}{20 x y} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{5 x^{-2} y (3 x y)^{2}}{20 x y}
$$

**Step-by-Step Simplification:**

1. **Expand $$(3 x y)^2$$:**
   
   $$
   (3 x y)^2 = 3^2 \cdot x^2 \cdot y^2 = 9 x^2 y^2
   $$

2. **Substitute back into the original expression:**
   
   $$
   \frac{5 x^{-2} y \cdot 9 x^2 y^2}{20 x y} = \frac{45 x^{-2} \cdot x^2 \cdot y \cdot y^2}{20 x y}
   $$

3. **Simplify the $$x$$ terms:**
   
   $$
   x^{-2} \cdot x^2 = x^{(-2 + 2)} = x^0 = 1
   $$

4. **Simplify the $$y$$ terms:**
   
   $$
   y \cdot y^2 = y^{1+2} = y^3
   $$

5. **Now, the expression becomes:**
   
   $$
   \frac{45 \cdot y^3}{20 x y} = \frac{45 y^3}{20 x y}
   $$

6. **Simplify the coefficients and the remaining $$y$$ terms:**
   
   - Coefficients: $$ \frac{45}{20} = \frac{9}{4} $$
   - $$ y^3 / y = y^{3-1} = y^2 $$

7. **Final Simplified Expression:**
   
   $$
   \frac{9 y^2}{4 x}
   $$

**Answer:**

$$
\frac{9\, y^{2}}{4\, x}
$$
$$ \frac{9\, y^{2}}{4\, x} $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions