Math Problem Statement

Evaluate the expression. (−6)3

Solution

To evaluate the expression (6)3(-6)^3, we need to cube the number 6-6.

This means:

(6)3=(6)×(6)×(6)(-6)^3 = (-6) \times (-6) \times (-6)

Now, calculate step by step:

  1. Multiply the first two terms:
    (6)×(6)=36(-6) \times (-6) = 36

  2. Then, multiply that result by the third 6-6:
    36×(6)=21636 \times (-6) = -216

Therefore, the value of (6)3(-6)^3 is 216\boxed{-216}.

Would you like further explanation on how to handle powers or any related concept? Let me know if you need more details!

Here are some related questions you might find interesting:

  1. What is the value of 636^3?
  2. How do negative exponents affect an expression?
  3. What happens if you cube a positive number like 6?
  4. How does the cube root of 216 relate to this problem?
  5. What is the general rule for evaluating negative numbers raised to powers?

Tip: When working with odd powers of negative numbers, the result will always be negative, while even powers of negative numbers will result in positive values.

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Math Problem Analysis

Mathematical Concepts

Exponents
Multiplication of Negative Numbers

Formulas

a^3 = a × a × a

Theorems

Exponentiation with negative numbers
Multiplication of negative numbers

Suitable Grade Level

Grades 6-8