https://file.aiquickdraw.com/mathbot/file/17254762205814sgb4xw5.jpg

The expression given is \(\left(p^2 q\right)^3\) with \(p = -4\) and \(q = 3\).

Let's solve this step by step:

1. **Substitute the values of \(p\) and \(q\) into the expression**:
   \[
   \left((-4)^2 \cdot 3\right)^3
   \]

2. **Calculate \((-4)^2\)**:
   \[
   (-4)^2 = 16
   \]

3. **Substitute this result into the expression**:
   \[
   \left(16 \cdot 3\right)^3
   \]

4. **Multiply 16 by 3**:
   \[
   16 \cdot 3 = 48
   \]

5. **Raise 48 to the power of 3**:
   \[
   48^3 = 48 \times 48 \times 48 = 110592
   \]

So, the value of the expression \(\left(p^2 q\right)^3\) for \(p = -4\) and \(q = 3\) is **110592**.

Would you like more details or have any questions?

---

Here are some related questions you might consider:

1. What would happen if the expression was \(\left(pq^2\right)^3\) instead?
2. How would the result change if \(p\) were positive, for example, \(p = 4\)?
3. What is the impact of the exponent 3 on the final result?
4. How would the result change if the exponent 3 were instead a different value, like 2?
5. What is the general rule for simplifying expressions like \(\left(p^m q^n\right)^k\)?

**Tip**: When dealing with exponents, always simplify the base expression first before applying the exponentiation.

What is the value of the expression \(\left(p^2 q\right)^3\) for \(p = -4\) and \(q = 3\)?

Learn how to evaluate the algebraic expression \(\left(p^2 q\right)^3\) for given values of p and q. This problem involves exponentiation and basic algebraic manipulation, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation