The value of $ 3^3 - 5^2 + \left(\frac{26}{13}\right)^2 - 8 + ... | Mathematics MCQ | Examoogle

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The value of $3^3 - 5^2 + \left(\frac{26}{13}\right)^2 - 8 + 0 \times 9 =$ ________

Correct Answer

📐 MA • Math Direct ArithmeticMathematicsSimplification

Option D

Quick Summary:

Evaluate terms sequentially using BODMAS/PEMDAS rule, noting that any term multiplied by 0 vanishes immediately.

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📐MAMath SolutionDirect Arithmetic

📋 Given

An arithmetic expression: 3³ - 5² + (26/ $13)^2$ - 8 + 0 * 9

🔢 Formula Used

an,(a/b)n,a×0=0a^n, \quad (a/b)^n, \quad a \times 0 = 0an,(a/b)n,a×0=0

⚡ Exam Hall Shortcut / Speed Trick

Evaluate terms sequentially using BODMAS/PEMDAS rule, noting that any term multiplied by 0 vanishes immediately.

⚠️ Common Student Trap / Pitfall

Confusing the order of operations or incorrectly calculating the power $(26/13)^2$ by failing to simplify the fraction inside the parentheses first.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Simplify exponent terms and fractions

Evaluate $3^3 = 27$ , $5^2 = 25$ , and the fraction inside the parenthesis $(26/13) = 2$ .

33=27,52=25,(2613)2=22=43^3 = 27, \quad 5^2 = 25, \quad \left(\frac{26}{13}\right)^2 = 2^2 = 433=27,52=25,(1326​)2=22=4

Simplify multiplication term

Apply the zero product property to the last term.

0×9=00 \times 9 = 00×9=0

Combine all terms

Substitute the simplified values into the original expression: $27 - 25 + 4 - 8 + 0$ .

27−25+4−8+0=2+4−8=6−8=−227 - 25 + 4 - 8 + 0 = 2 + 4 - 8 = 6 - 8 = -227−25+4−8+0=2+4−8=6−8=−2

✅

D is correct because the final evaluation of the expression $27 - 25 + 4 - 8 + 0$ results in $-2$ .

Core Concepts Used

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BODMAS Rule Exponent Laws Arithmetic Operations

💡 EXAM TIP

Always simplify fractions inside parentheses before applying powers to make the calculation significantly easier and reduce the chance of manual error.

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