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GATE 2025 EE – Question 5

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 1 mark · Multiple choice

What is the value of $\left(\dfrac{3^{81}}{27^4}\right)^{\frac13}$ ?

  1. $3^{13}$
  2. $3^{96}$
  3. $3^{23}$
  4. $3^{69}$

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Show answer and explanation

Correct answer: (C) $3^{23}$

Explanation

$27^4=3^{12}$, so the fraction is $3^{81-12}=3^{69}$. Then $(3^{69})^{1/3}=3^{23}$.