Let's break this down step by step:

The expression is:

\[
-7^3 + (-3)^4
\]

1. **First part: \( -7^3 \)**

\[
7^3 = 7 \times 7 \times 7 = 343
\]
Since the negative sign is in front of the cube:

\[
-7^3 = -343
\]

2. **Second part: \( (-3)^4 \)**

\[
(-3)^4 = (-3) \times (-3) \times (-3) \times (-3) = 81
\]

Now, putting it all together:

\[
-343 + 81 = -262
\]

Thus, the final result is:

\[
-262
\]

Would you like more details or explanations?

Here are 5 related questions to explore further:

1. What is the difference between \((-3)^4\) and \(-3^4\)?
2. How does the order of operations affect the result in expressions with exponents?
3. What happens if you cube a negative number? Why is the result negative?
4. How do even and odd powers of negative numbers differ?
5. What role do parentheses play in evaluating expressions with negative numbers?

**Tip:** Always handle exponents first in expressions following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Learn how to evaluate the expression -7³ + (-3)⁴ by breaking down the steps involving exponents and negative numbers. This example follows the order of operations and highlights key concepts like handling negative bases with exponents. Suitable for students in Grades 7-9.

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