Math Problem Statement

-3⁰-3²-2(-2-3)

Solution

Let's solve the expression step by step.

The given expression is:

30[322(23)](20)-3^0 \left[-3^2 - 2(-2 - 3)\right](-2^0)

Step 1: Evaluate the exponents

  1. 30-3^0: 30=1(since any non-zero number raised to the power of 0 is 1, and the negative sign remains)-3^0 = -1 \quad \text{(since any non-zero number raised to the power of 0 is 1, and the negative sign remains)}

  2. 32-3^2: 32=9(square the number 3 first, then apply the negative sign)-3^2 = -9 \quad \text{(square the number 3 first, then apply the negative sign)}

  3. 20-2^0: -2^0 = -1 \quad \text{(similar to -3^0)}

Step 2: Simplify inside the brackets [322(23)]\left[-3^2 - 2(-2 - 3)\right]

  1. Evaluate the expression inside the parentheses (23)(-2 - 3): 23=5-2 - 3 = -5

  2. Multiply by 2-2: 2(5)=102(-5) = -10

  3. Combine the results: 9(10)=9+10=1-9 - (-10) = -9 + 10 = 1

Step 3: Combine everything

Now, the expression is simplified to: (1)(1)(1)(-1)(1)(-1)

Step 4: Final multiplication

Multiply these values together: (1)×1×(1)=1(-1) \times 1 \times (-1) = 1

So, the final result is:

1\boxed{1}

Would you like more details or have any questions?


Here are five related questions to expand your understanding:

  1. How does the order of operations affect the result in this expression?
  2. Why do negative exponents have different rules compared to positive exponents?
  3. How would the expression change if the powers were even numbers?
  4. What happens if the base of an exponent is a fraction?
  5. How can understanding negative and zero exponents help in solving algebraic equations?

Tip: Always pay attention to the order of operations (PEMDAS/BODMAS) when solving complex expressions.

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Math Problem Analysis

Mathematical Concepts

Exponents
Order of Operations
Negative Numbers

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9