Math Problem Statement

Evaluate the expression.

open parentheses negative 7 close parentheses to the power of 4

Solution

To evaluate (7)4(-7)^4, follow these steps:

(7)4=(7)×(7)×(7)×(7)(-7)^4 = (-7) \times (-7) \times (-7) \times (-7)

  1. First, multiply the first two factors: (7)×(7)=49(-7) \times (-7) = 49

  2. Then, multiply the next two factors: 49×(7)=34349 \times (-7) = -343

  3. Finally, multiply by the last 7-7: 343×(7)=2401-343 \times (-7) = 2401

Therefore, (7)4=2401(-7)^4 = 2401.

Would you like more details on the steps or any other clarifications?

Here are 5 related questions for practice:

  1. What is (3)5(-3)^5?
  2. How would you evaluate (2)6(-2)^6?
  3. What is (4)3(-4)^3?
  4. How does the sign change when raising negative numbers to even vs odd powers?
  5. What is (5)2+(5)3(-5)^2 + (-5)^3?

Tip: When raising a negative number to an even power, the result is always positive.

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Numbers
Powers

Formulas

a^n where a is the base and n is the exponent

Theorems

Multiplication of negative numbers
Even powers of negative numbers

Suitable Grade Level

Grades 6-8