Evaluate  (−4)6·(−3)2
. Write your answer as an integer.

To evaluate the expression \((-4)^6 \cdot (-3)^2\), we can follow these steps:

1. **Evaluate \((-4)^6\):**
   \[
   (-4)^6 = (-4) \times (-4) \times (-4) \times (-4) \times (-4) \times (-4)
   \]
   Since multiplying an even number of negative factors results in a positive number:
   \[
   (-4)^6 = 4096
   \]

2. **Evaluate \((-3)^2\):**
   \[
   (-3)^2 = (-3) \times (-3)
   \]
   Multiplying two negative factors gives a positive result:
   \[
   (-3)^2 = 9
   \]

3. **Multiply the results:**
   \[
   4096 \times 9 = 36864
   \]

So, the final answer is \( \boxed{36864} \).

Would you like any details or have any questions? Here are some related questions:

1. How do you evaluate powers of negative numbers in general?
2. What is the result of \((-2)^8\)?
3. How does the sign of the base affect the result when raised to an odd power?
4. Can you explain why \((-4)^6\) and \((-4) \times 6\) are different?
5. What happens when you raise a negative number to a fractional exponent?

**Tip:** When raising a negative number to a power, remember that an even exponent results in a positive value, while an odd exponent results in a negative value.

Learn how to evaluate the expression (-4)^6 * (-3)^2 with a detailed step-by-step solution. Understand the rules for exponents and negative numbers. Suitable for students in Grades 7-9.

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