Fully simplify using only positive exponents. $$ \frac{3 x^{8} y^{7}}{6 x^{6} y^{3}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$\frac{3 x^{8} y^{7}}{6 x^{6} y^{3}}$$ using only positive exponents, follow these steps:

1. **Simplify the coefficients:**
   $$
   \frac{3}{6} = \frac{1}{2}
   $$

2. **Simplify the $$x$$-terms:**
   $$
   \frac{x^{8}}{x^{6}} = x^{8-6} = x^{2}
   $$

3. **Simplify the $$y$$-terms:**
   $$
   \frac{y^{7}}{y^{3}} = y^{7-3} = y^{4}
   $$

4. **Combine the simplified parts:**
   $$
   \frac{1}{2} x^{2} y^{4} \quad \text{or} \quad \frac{x^{2} y^{4}}{2}
   $$

Both forms are correct, but typically the expression is written with the constant in the denominator:

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

**Final Answer:**
$$
\frac{x^{2} y^{4}}{2}
$$
$$ \frac{x^{2} y^{4}}{2} $$

Fully simplify using only positive exponents. \[ \frac{3 x^{8} y^{7}}{6 x^{6} y^{3}} \]