Compare the following pairs of numbers

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Compare the following pairs of numbers. In each case, state which number is greater (or if they are equal) and give a clear reason without expanding the numbers into their full decimal form. (i)

5^{-3}

and

3^{-5}

(ii)

4^{2/3}

and

2^{4/3}

(iii)

\left(\dfrac12\right)^{-4}

and

2^{4}

Related theory

Laws of Exponents
Real Number System
Laws of exponents for real numbers
Number Systems

Browse the problem library