Math Problem Statement

(-3)^4

Solution

The expression visible in the image is (3)4(-3)^4.

Let's solve it step by step:

  1. When raising a negative number to an even power, the result is positive.
  2. (3)4=(3)×(3)×(3)×(3)(-3)^4 = (-3) \times (-3) \times (-3) \times (-3)
  3. The result of this is: (3)×(3)=9(-3) \times (-3) = 9 9×(3)=279 \times (-3) = -27 27×(3)=81-27 \times (-3) = 81

So, (3)4=81(-3)^4 = 81.

Let me know if you'd like further details or have any other questions.

Here are 5 questions based on this:

  1. What is the result of (2)5(-2)^5?
  2. How do powers of negative numbers change with odd vs even exponents?
  3. Can you explain why (1)n(-1)^n equals 1 or -1 depending on nn?
  4. What happens if the negative sign is outside the parentheses in 34-3^4?
  5. How do powers of fractions work with negative bases?

Tip: When dealing with negative numbers raised to a power, always check if the exponent is even or odd—this determines whether the result will be positive or negative!

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Math Problem Analysis

Mathematical Concepts

Exponents
Negative Numbers
Algebra

Formulas

(-a)^n = a^n when n is even

Theorems

Exponentiation of negative numbers
Even vs. odd powers of negative numbers

Suitable Grade Level

Grades 6-8