Solve the equation: (10 + 2) × (82 + 4) × (142 + 2) / 4 = ?

2023

Solve the equation: (10 + 2) × (82 + 4) × (142 + 2) / 4 = ?

  1. A.

    40, 536

  2. B.

    40,392

  3. C.

    40899

  4. D.

    None of the above

Show answer & explanation

Correct answer: B

Concept: To evaluate a numerical expression containing exponents, brackets, multiplication, and division, follow the standard order of operations — first evaluate any exponents, then simplify the arithmetic inside each bracket, and finally carry out multiplication and division working left to right.

  1. Evaluate the exponents: 82 = 64 and 142 = 196.

  2. Substitute back into each bracket: (10 + 2) = 12, (64 + 4) = 68, and (196 + 2) = 198.

  3. Multiply the three bracket results in order: 12 × 68 = 816, then 816 × 198 = 161,568.

  4. Divide by 4: 161,568 / 4 = 40,392.

Cross-check: divide 68 by 4 first (68 / 4 = 17), then multiply: 12 × 17 × 198 = 40,392 — the same result, confirming the answer.

So the value of the expression is 40,392.

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