https://file.aiquickdraw.com/mathbot/file/1726309983656lydmj6zr.jpeg

The expression provided in the image is:

\[
\left( -1 \frac{1}{2} \right)^3
\]

This is a mixed fraction, \( -1 \frac{1}{2} \), raised to the power of 3. We can first convert the mixed fraction into an improper fraction, then apply the exponent.

### Step 1: Convert to an improper fraction
\( -1 \frac{1}{2} \) can be rewritten as \( -\frac{3}{2} \).

### Step 2: Apply the exponent
We now raise \( -\frac{3}{2} \) to the power of 3:

\[
\left( -\frac{3}{2} \right)^3 = \frac{(-3)^3}{2^3} = \frac{-27}{8}
\]

Thus, the result is:

\[
\boxed{-\frac{27}{8}}
\]

Would you like any additional explanation or details?

Here are 5 related questions to expand on this:
1. How do you convert mixed numbers to improper fractions?
2. What is the general rule for raising a fraction to a power?
3. How does the negative sign affect the result when raising a number to an odd power?
4. Can you express \( -\frac{27}{8} \) as a mixed number?
5. What happens if the exponent is an even number instead of 3?

**Tip:** When dealing with mixed numbers, always convert them to improper fractions first to make exponentiation easier.

Learn how to raise a mixed number (-1 1/2) to the power of 3. This problem explores exponentiation, conversion of mixed numbers to improper fractions, and properties of negative exponents. Detailed solution for students in Grades 6-8.

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