how do you get the -32*π*^2 from (-1/2)(8*π*)^2

To simplify \((- \frac{1}{2})(8\pi)^2\) and arrive at \(-32\pi^2\), follow these steps:

1. **Square the term inside the parentheses:**
   \[
   (8\pi)^2 = 8^2 \times \pi^2 = 64\pi^2
   \]

2. **Multiply by \(- \frac{1}{2}\):**
   \[
   - \frac{1}{2} \times 64\pi^2 = -\frac{64\pi^2}{2} = -32\pi^2
   \]

So, \((- \frac{1}{2})(8\pi)^2 = -32\pi^2\).

Would you like further details or have any other questions?

Here are five related questions:
1. How do you simplify expressions involving exponents and coefficients?
2. What is the general rule for squaring a product of numbers and variables?
3. How does multiplying a fraction by a whole number work?
4. Can you explain the distribution of multiplication over addition and subtraction?
5. What is the significance of \(\pi^2\) in mathematical equations?

**Tip:** Always apply the exponent to both the coefficient and the variable when squaring an expression like \( (8\pi)^2 \).

Learn how to simplify the expression (-1/2)(8π)^2 to -32π^2 with a step-by-step explanation. This problem involves exponents, coefficients, and multiplication of fractions. Suitable for students in Grades 7-9.

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