https://file.aiquickdraw.com/mathbot/file/1726538979809iqa2gc2a.jpg

The mathematical expression from the image is:

\[
\left\{ \frac{(-2)^3}{[2 - (-2)^2]} \right\} - \left\{ \frac{[15 - 3]}{2 - 8} \right\}
\]

Let's break this down step by step.

### Left side expression:
\[
\frac{(-2)^3}{2 - (-2)^2}
\]
- \( (-2)^3 = -8 \)
- \( (-2)^2 = 4 \), so \( 2 - 4 = -2 \)

Thus, the left side simplifies to:
\[
\frac{-8}{-2} = 4
\]

### Right side expression:
\[
\frac{15 - 3}{2 - 8}
\]
- \( 15 - 3 = 12 \)
- \( 2 - 8 = -6 \)

Thus, the right side simplifies to:
\[
\frac{12}{-6} = -2
\]

### Final step:
Now subtract the two results:
\[
4 - (-2) = 4 + 2 = 6
\]

So the final result of the entire expression is **6**.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Simplify \( \frac{(-3)^4}{3 - (-3)^2} \).
2. Evaluate \( \frac{7 - 2^2}{5 - (-2)^3} \).
3. Calculate \( \frac{4^3}{9 - 2^2} \).
4. Find the result of \( 5 - \frac{12}{4 - (-2)^2} \).
5. Simplify \( \left\{ \frac{(-5)^2}{3 - (-1)^2} \right\} - \left\{ \frac{10}{4 - (-6)} \right\} \).

**Tip**: Always handle exponents and parentheses first in expressions to avoid errors!

{((-2)^3 / [2 - (-2)^2]) - ([15 - 3] / [2 - 8])}

This problem demonstrates how to simplify a mathematical expression involving exponents and fractions: {((-2)^3 / [2 - (-2)^2]) - ([15 - 3] / [2 - 8])}. Learn step-by-step solutions, including handling exponents and negative numbers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation