Math Problem Statement

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

Solution

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

  1. Evaluate (4)6(-4)^6: (4)6=(4)×(4)×(4)×(4)×(4)×(4)(-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(-4)^6 = 4096

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

  3. Multiply the results: 4096×9=368644096 \times 9 = 36864

So, the final answer is 36864\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(-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(-4)^6 and (4)×6(-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.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative numbers
Multiplication of powers

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9