Let's solve the expression step by step:

Given expression:  
\[
(-3)^3 - 2(-3)^2 + 5(-3) - 7
\]

### Step 1: Calculate \((-3)^3\)
\[
(-3)^3 = -27
\]

### Step 2: Calculate \((-3)^2\)
\[
(-3)^2 = 9
\]
Now substitute it back into the expression:
\[
-27 - 2(9) + 5(-3) - 7
\]

### Step 3: Simplify the terms
\[
-27 - 18 + (-15) - 7
\]

### Step 4: Combine the terms
\[
-27 - 18 - 15 - 7 = -67
\]

So, the final answer is:
\[
\boxed{-67}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you calculate powers of negative numbers?
2. Why does \((-3)^2\) become positive, but \((-3)^3\) remains negative?
3. How do parentheses affect operations in an expression?
4. What are some tips for simplifying multi-term expressions like this?
5. Can you provide more examples involving negative numbers and powers?

**Tip:** Always apply exponents and distribute terms carefully to avoid mistakes with signs!

Discover how to solve the algebraic expression (-3)^3 - 2(-3)^2 + 5(-3) - 7. This solution covers key algebraic concepts like exponents, order of operations, and negative numbers, providing a step-by-step guide to simplify multi-term expressions. Perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation