Simplify the following expression. Write the result using positive exponents only. Assume t $$ \frac{-18 a^{6} b}{9 a b^{7}} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression $$\frac{-18 a^{6} b}{9 a b^{7}}$$ and write it using positive exponents only, follow these steps:

1. **Simplify the coefficients:**
   $$
   \frac{-18}{9} = -2
   $$

2. **Simplify the $$a$$ terms:**
   $$
   \frac{a^6}{a} = a^{6-1} = a^5
   $$

3. **Simplify the $$b$$ terms:**
   $$
   \frac{b}{b^7} = b^{1-7} = b^{-6} = \frac{1}{b^6}
   $$

4. **Combine the results:**
   $$
   -2 \cdot a^5 \cdot \frac{1}{b^6} = \frac{-2a^5}{b^6}
   $$

Therefore, the simplified expression with positive exponents is:

$$
\boxed{\dfrac{-2a^{5}}{b^{6}}}
$$
$$\frac{-2a^{5}}{b^{6}}$$

Simplify the following expression. Write the result using positive exponents only. Assume t \( \frac{-18 a^{6} b}{9 a b^{7}} \)