Mathematics

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. a. (i)

5^{-3}

and

3^{-5}

b. (ii)

4^{2/3}

and

2^{4/3}

c. (iii)

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

and

2^{4}

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