A mixed computation combines signed arithmetic with grouping and powers. Separate the order of operations from the sign rules so that each step has a clear reason.

A reliable method

  1. Simplify parentheses while retaining negative signs.
  2. Evaluate powers with the stated base.
  3. Complete signed multiplication and division.
  4. Combine the remaining signed terms and check by estimation.

Example 1

Evaluate \(-5+3\times \left(-4\right)\) exactly.

  1. Apply one operation at a time, keeping the sign on each number:
  2. \(-5+3\times \left(-4\right)\) = \(-5-12\).
  3. \(-5-12\) = \(-17\).
  4. The final exact answer is \(-17\).

Answer: \(-17\)

Example 2

Evaluate \(\left(-3\right)^{2}-\left(2\times 7\right)\) exactly.

  1. Apply one operation at a time, keeping the sign on each number:
  2. \(\left(-3\right)^{2}-\left(2\times 7\right)\) = \(9-14\).
  3. \(9-14\) = \(-5\).
  4. The final exact answer is \(-5\).

Answer: \(-5\)

Common mistakes

  • The minus sign outside a square is not part of the squared base.
  • When subtracting a grouped expression, reverse every sign inside if removing the grouping.

Practice without the answer first

  1. Evaluate \(\frac{24}{-6}-\left(-8\right)\) exactly.
  2. Evaluate \(7-\left(2-9\right)\) exactly.
  3. Evaluate \(\left(-2\right)^{3}+\frac{18}{3}\) exactly.
Answers and step-by-step explanations

Practice 1

  1. Apply one operation at a time, keeping the sign on each number:
  2. \(\frac{24}{-6}-\left(-8\right)\) = \(-4+8\).
  3. \(-4+8\) = \(4\).
  4. The final exact answer is \(4\).

Answer: \(4\)

Practice 2

  1. Apply one operation at a time, keeping the sign on each number:
  2. \(7-\left(2-9\right)\) = \(7-\left(-7\right)\).
  3. \(7-\left(-7\right)\) = \(14\).
  4. The final exact answer is \(14\).

Answer: \(14\)

Practice 3

  1. Apply one operation at a time, keeping the sign on each number:
  2. \(\left(-2\right)^{3}+\frac{18}{3}\) = \(-8+6\).
  3. \(-8+6\) = \(-2\).
  4. The final exact answer is \(-2\).

Answer: \(-2\)

Study context: This shared lesson supports math study across exams. Use it to repair a prerequisite or practice the matching skill; it is not an official SAT question set or a score prediction.

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