Evaluate a3- 5b + b ÷ ac for a = -2, b = 6, and
с = 3.

We are given the expression:

\[
a^3 - 5b + \frac{b}{ac}
\]

We need to substitute the values \( a = -2 \), \( b = 6 \), and \( c = 3 \) into this expression. Let's break it down step by step:

1. **Substitute the values**:
   \[
   a^3 - 5b + \frac{b}{ac} = (-2)^3 - 5(6) + \frac{6}{(-2)(3)}
   \]

2. **Evaluate each term**:
   - \( (-2)^3 = -8 \)
   - \( -5(6) = -30 \)
   - \( \frac{6}{(-2)(3)} = \frac{6}{-6} = -1 \)

3. **Combine everything**:
   \[
   -8 - 30 - 1 = -39
   \]

So, the value of the expression is:

\[
\boxed{-39}
\]

Would you like more details or have any other questions?

Here are some related questions to expand your understanding:
1. What happens if \( a = 0 \) in the expression?
2. How would the result change if \( c = -3 \)?
3. What would the outcome be if we added an additional \( b^2 \) term to the expression?
4. How can this expression be rewritten in terms of common factors of \( a \) and \( b \)?
5. How would the evaluation change if \( b = -6 \) and \( a = 2 \)?

**Tip:** Always apply order of operations (PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction) to simplify complex expressions.

Evaluate a^3 - 5b + b ÷ ac for a = -2, b = 6, and c = 3.

Learn how to evaluate the algebraic expression a^3 - 5b + b ÷ ac with step-by-step instructions using the values a = -2, b = 6, and c = 3. This problem involves concepts like exponentiation, substitution, and basic arithmetic operations, making it suitable for students in Grades 8-10.

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