Ratio, Proportion, Indices, LogarithmMCQPYQ Jan 21Question 880 of 305
All Questions

Find the value of 3t−1/t−1/3\displaystyle 3t^{-1} / t^{-1/3}

Options

A3t2/3\displaystyle \frac{3}{t^{2/3}}
B3t3/2\displaystyle \frac{3}{t^{3/2}}
C3t1/3\displaystyle \frac{3}{t^{1/3}}
D3t2\displaystyle \frac{3}{t^2}
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Correct Answer

✅ Option a — 3t2/3\displaystyle \frac{3}{t^{2/3}}

All Options:

  • A3t2/3\displaystyle \frac{3}{t^{2/3}}
  • B3t3/2\displaystyle \frac{3}{t^{3/2}}
  • C3t1/3\displaystyle \frac{3}{t^{1/3}}
  • D3t2\displaystyle \frac{3}{t^2}

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Detailed Solution & Explanation

We want to simplify the expression:
3t−1t−13\frac{3t^{-1}}{t^{-\frac{1}{3}}}
Using the laws of exponents (xaxb=xa−b\displaystyle \frac{x^a}{x^b} = x^{a-b}):
3t−1t−13=3⋅t−1−(−13)\frac{3t^{-1}}{t^{-\frac{1}{3}}} = 3 \cdot t^{-1 - \left(-\frac{1}{3}\right)}
Simplify the exponent:
−1−(−13)=−1+13=−23-1 - \left(-\frac{1}{3}\right) = -1 + \frac{1}{3} = -\frac{2}{3}
Substituting this back into the expression:
3⋅t−23=3t233 \cdot t^{-\frac{2}{3}} = \frac{3}{t^{\frac{2}{3}}}
This matches **Option A**.
Note: The textbook answer key incorrectly specifies **Option B** as correct. However, our mathematical derivation shows that the simplified form is 3t2/3\displaystyle \frac{3}{t^{2/3}} (Option A).
Hence, **Option A** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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