If P = 2, Q = 3, R = 5, find the value of P^R - Q^P. | Mathematics MCQ | Examoogle

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If P = 2, Q = 3, R = 5, find the value of Pᴿ - Qᴾ.

Correct Answer

📐 MA • Math Direct SubstitutionMathematicsMathematics

Option A

Quick Summary:

Calculate powers individually: $2^5$ is doubling 2 five times (32) and $3^2$ is 3 $\times 3 (9).$ Simply subtract 9 from 32.

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📐MAMath SolutionDirect Substitution

📋 Given

Variables are defined as P = 2, Q = 3, and R = 5.

🔢 Formula Used

Result=PR−QP\text{Result} = P^R - Q^PResult=PR−QP

⚡ Exam Hall Shortcut / Speed Trick

Calculate powers individually: $2^5$ is doubling 2 five times (32) and $3^2$ is 3 $\times 3 (9).$ Simply subtract 9 from 32.

⚠️ Common Student Trap / Pitfall

Students often swap the exponent and the base, calculating $R^P$ instead of $P^R$ , or miscalculating $2^5$ as $2 \times 5 = 10$ .

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Substitute the values into the expression

Replace P, Q, and R with their given numerical values in the expression $P^R - Q^P$ .

25−322^5 - 3^225−32

Evaluate the exponents

Calculate $2^5$ as $2 \times 2 \times 2 \times 2 \times 2 = 32$ and $3^2$ as $3 \times 3 = 9$ .

32−932 - 932−9

Perform the subtraction

Subtract the value of $Q^P$ from $P^R$ .

32−9=2332 - 9 = 2332−9=23

✅

A is correct because substituting the values $P=2, Q=3, R=5$ into the expression yields $2^5 - 3^2 = 32 - 9 = 23$ .

Core Concepts Used

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Exponents Substitution Order of operations

💡 EXAM TIP

This basic algebraic substitution is the foundation for solving complex polynomial evaluations and function notation problems in calculus.

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