https://file.aiquickdraw.com/mathbot/file/172948473774437f0zzq2.jpg

Let's simplify the expression in question.

The problem asks to simplify the following expression:

\[
\frac{24a^{-7}b^{-2}c}{6a^{-2}b^{-3}c^{-6}}
\]

### Step-by-step simplification:

1. **Simplify the coefficient**: 
   \[
   \frac{24}{6} = 4
   \]

2. **Simplify the powers of \(a\)** using the rule \( \frac{a^m}{a^n} = a^{m-n} \):
   \[
   \frac{a^{-7}}{a^{-2}} = a^{-7 - (-2)} = a^{-7 + 2} = a^{-5}
   \]

3. **Simplify the powers of \(b\)**:
   \[
   \frac{b^{-2}}{b^{-3}} = b^{-2 - (-3)} = b^{-2 + 3} = b^{1}
   \]

4. **Simplify the powers of \(c\)**:
   \[
   \frac{c}{c^{-6}} = c^{1 - (-6)} = c^{1 + 6} = c^{7}
   \]

Now, put everything together:

\[
\frac{24a^{-7}b^{-2}c}{6a^{-2}b^{-3}c^{-6}} = 4a^{-5}b^{1}c^{7}
\]

### Final Answer:
The simplified form is:
\[
4a^{-5}bc^{7}
\]

Looking at the answer choices in the image, the correct answer is **d. \( \frac{4bc^7}{a^5} \)**.

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Do you need further details or have any questions?

Here are some related questions:
1. How do we handle negative exponents in simplifications?
2. What other exponent rules are useful in simplifying expressions?
3. Can you explain the quotient rule for exponents?
4. Why did we subtract exponents when dividing like bases?
5. How would the solution change if one of the exponents were a fraction?

**Tip:** Always double-check exponent signs, especially when adding or subtracting them. Misinterpreting a negative exponent can lead to mistakes!

Bentuk sederhana dari \(\frac{24a^{-7}b^{-2}c}{6a^{-2}b^{-3}c^{-6}}\) adalah ...

Simplify the algebraic expression \(\frac{24a^{-7}b^{-2}c}{6a^{-2}b^{-3}c^{-6}}\) by using exponent rules. Learn the step-by-step process to simplify the terms and combine exponents to arrive at the final form. This solution is ideal for high school students studying exponents and rational expressions.

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