Fully simplify using only positive exponents. $$ \frac{27 x y^{3}}{3 x^{8} y^{7}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$\frac{27 x y^{3}}{3 x^{8} y^{7}}$$ using only positive exponents, follow these steps:

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

2. **Simplify the $$x$$ terms:**
   $$
   \frac{x}{x^8} = x^{1-8} = x^{-7} = \frac{1}{x^7}
   $$

3. **Simplify the $$y$$ terms:**
   $$
   \frac{y^3}{y^7} = y^{3-7} = y^{-4} = \frac{1}{y^4}
   $$

4. **Combine all simplified parts:**
   $$
   9 \times \frac{1}{x^7} \times \frac{1}{y^4} = \frac{9}{x^7 y^4}
   $$

So, the fully simplified expression using only positive exponents is:

$$
\frac{9}{x^{7} y^{4}}
$$
$$ \frac{9}{x^{7} y^{4}} $$

Fully simplify using only positive exponents.