https://file.aiquickdraw.com/mathbot/file/17267931479418ytbfpq1.jpg

The expression provided in the image is:

\[
\frac{24a^3 b^{-2} c^5}{8a^{-2} b c^3}
\]

We are asked to simplify this expression into a form where all exponents are positive.

### Step-by-Step Solution:

1. **Simplify the constants**:  
   \[
   \frac{24}{8} = 3
   \]

2. **Simplify the powers of \(a\)**:  
   \[
   a^3 \div a^{-2} = a^{3 - (-2)} = a^{3 + 2} = a^5
   \]

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

4. **Simplify the powers of \(c\)**:  
   \[
   c^5 \div c^3 = c^{5 - 3} = c^2
   \]

### Putting it all together:

\[
3a^5 b^{-3} c^2
\]

To make all exponents positive, move \(b^{-3}\) to the denominator:

\[
3a^5 c^2 \div b^3
\]

Thus, the simplified expression in terms of positive exponents is:

\[
\frac{3a^5 c^2}{b^3}
\]

Would you like further clarification on any part of the solution? Here are some related questions to deepen understanding:

1. How do you handle negative exponents in general?
2. What rules govern the division of exponents with the same base?
3. How do constant coefficients behave in algebraic fractions?
4. Can this process be extended to expressions with more variables?
5. How would you simplify an expression involving radicals instead of exponents?

**Tip:** Always remember that negative exponents indicate a reciprocal, so moving terms to the denominator or numerator is key to ensuring positive exponents.

Bentuk pangkat positif dari \( \frac{24a^3 b^{-2} c^5}{8a^{-2} b c^3} \) adalah ...

Learn how to simplify the expression \( \frac{24a^3 b^{-2} c^5}{8a^{-2} b c^3} \) to a form where all exponents are positive. This step-by-step solution covers algebraic rules for exponents, including simplifying constants, handling negative exponents, and dividing powers with the same base.

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