Simplify: $$ \frac{\left(3 x^{2} y^{2}\right)^{2}}{3^{3} x^{2} y^{3}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$ \frac{\left(3 x^{2} y^{2}\right)^{2}}{3^{3} x^{2} y^{3}} $$, follow these steps:

1. **Expand the numerator:**
   $$
   \left(3 x^{2} y^{2}\right)^{2} = 3^{2} x^{4} y^{4} = 9 x^{4} y^{4}
   $$

2. **Write the denominator:**
   $$
   3^{3} x^{2} y^{3} = 27 x^{2} y^{3}
   $$

3. **Form the fraction:**
   $$
   \frac{9 x^{4} y^{4}}{27 x^{2} y^{3}}
   $$

4. **Simplify the coefficients:**
   $$
   \frac{9}{27} = \frac{1}{3}
   $$

5. **Simplify the variables by subtracting exponents:**
   $$
   x^{4} / x^{2} = x^{2}
   $$
   $$
   y^{4} / y^{3} = y
   $$

6. **Combine the simplified parts:**
   $$
   \frac{1}{3} x^{2} y
   $$

**Final Simplified Form:**
$$
\frac{x^{2} y}{3}
$$

Answer: $$ \dfrac{x^{2}\, y}{3} $$
The simplified form of the expression is $$ \frac{x^{2} y}{3} $$.

Simplify: \( \frac{\left(3 x^{2} y^{2}\right)^{2}}{3^{3} x^{2} y^{3}} \)