Math Problem Statement

Evaluate abc^2 if a = -3, b = 6, and c = -8.

Solution

To evaluate abc2abc^2 given a=3a = -3, b=6b = 6, and c=8c = -8, we substitute these values into the expression:

abc2=(3)(6)((8)2)abc^2 = (-3)(6)((-8)^2)

Step 1: Evaluate c2c^2

(8)2=64(-8)^2 = 64

Step 2: Multiply the results

abc2=(3)(6)(64)abc^2 = (-3)(6)(64)

Step 3: Calculate step-by-step

  • (3)(6)=18(-3)(6) = -18
  • (18)(64)=1152(-18)(64) = -1152

Final Answer:

abc2=1152abc^2 = -1152

Let me know if you want further clarification or details.


Here are some related questions to deepen your understanding:

  1. What happens if one of the variables is zero in the expression abc2abc^2?
  2. How does the exponent affect the result when the base is negative, such as (8)2(-8)^2?
  3. What is the difference between evaluating abc2abc^2 and a2b2c2a^2b^2c^2?
  4. How would the result change if cc were a positive value?
  5. Can you write abc2abc^2 in terms of powers and solve it for any general values of a,b,ca, b, c?

Tip: Always simplify exponents first before handling the multiplications to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Multiplication

Formulas

abc^2 = a * b * (c^2)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 6-8