https://file.aiquickdraw.com/mathbot/file/1728952438082ncuqijn2.jpg

The expression in the image is:

\[
\frac{-16a^9}{8a^4}
\]

To simplify this, we'll divide both the coefficients and the variables separately.

### Step 1: Divide the coefficients
The coefficients are \(-16\) and \(8\). Dividing \(-16\) by \(8\):

\[
\frac{-16}{8} = -2
\]

### Step 2: Apply the rules of exponents
For the variables \(a^9\) and \(a^4\), apply the quotient rule of exponents:

\[
a^{9-4} = a^5
\]

### Step 3: Combine the results
Putting it all together:

\[
\frac{-16a^9}{8a^4} = -2a^5
\]

So, the simplified expression is:

\[
-2a^5
\]

Would you like a detailed explanation or have any other questions?

Here are some related questions:
1. What are the rules for dividing variables with exponents?
2. How do you simplify an expression involving negative coefficients?
3. How would the result change if the exponent in the denominator was higher than in the numerator?
4. What happens if the expression includes more variables, such as \( b \) or \( c \)?
5. Can you apply these rules when the variables are raised to negative exponents?

**Tip:** Always simplify the coefficients first before applying the rules of exponents to keep the process organized.

Learn how to simplify the algebraic expression -16a^9 / 8a^4 by dividing coefficients and applying the quotient rule of exponents. This problem covers key concepts in algebra and exponent rules, suitable for students in Grades 7-9.

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