The value of $ 4^2 - 3^3 + (20 / 4)^2 - 5 + 0 \times 7 $ is: | Mathematics MCQ | Examoogle

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The value of $4^2 - 3^3 + (20 / 4)^2 - 5 + 0 \times 7$ is:

Correct Answer

📐 MA • Math BODMAS RuleMathematicsSimplification

Option A

Quick Summary:

Calculate powers and divisions first. Recognize that $0 \times 7 = 0$ immediately to simplify the tail end of the expression.

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📐MAMath SolutionBODMAS Rule

📋 Given

A numerical expression $4^2 - 3^3 + (20 / 4)^2 - 5 + 0 \times 7$ .

🔢 Formula Used

BODMAS:Brackets,Orders,Division,Multiplication,Addition,SubtractionBODMAS: \text{Brackets}, \text{Orders}, \text{Division}, \text{Multiplication}, \text{Addition}, \text{Subtraction}BODMAS:Brackets,Orders,Division,Multiplication,Addition,Subtraction

⚡ Exam Hall Shortcut / Speed Trick

Calculate powers and divisions first. Recognize that $0 \times 7 = 0$ immediately to simplify the tail end of the expression.

⚠️ Common Student Trap / Pitfall

Students often miscalculate $3^3$ as $3 \times 3 = 9$ instead of $3 \times 3 \times 3 = 27$ , or they subtract before adding, which violates the additive priority in order of operations.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Evaluate Powers and Brackets

Calculate the exponent terms and the expression inside the parentheses: $4^2 = 16$ , $3^3 = 27$ , and $(20 / 4) = 5$ .

16−27+52−5+016 - 27 + 5^2 - 5 + 016−27+52−5+0

Simplify Exponent

Solve the remaining square term: $5^2 = 25$ .

16−27+25−5+016 - 27 + 25 - 5 + 016−27+25−5+0

Perform Addition and Subtraction

Group the positive and negative terms: $(16 + 25) - (27 + 5) = 41 - 32$ .

41−32=941 - 32 = 941−32=9

Final Correction/Verification

Wait, evaluating $16 - 27 + 25 - 5$ : $16 - 27 = -11$ . Then $-11 + 25 = 14$ . Finally $14 - 5 = 9$ .

16−27+25−5=916 - 27 + 25 - 5 = 916−27+25−5=9

✅

The expression evaluates to 9, which suggests a mismatch in the provided options. Based on the standard BODMAS arithmetic provided by the question, the result is 9.

Core Concepts Used

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BODMAS order of operations Exponentiation Arithmetic simplification

💡 EXAM TIP

This fundamental order of operations is the bedrock for solving complex algebraic expressions in Algebra and Data Interpretation questions.

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