Question

Why do we do for example 2 raised to the power of -2 so why do we write $\frac{1}{4}$?

Answer 1

Check the pattern
$2^5=2\times 2\times 2\times 2\times 22^4=2\times 2\times 2\times 2=\frac{2^5}{2}as,\frac{2^5}{2}=\frac{2\times 2\times 2\times 2\times 2\times \text{/}2}{\text{/}2}=2^4$
Similarly, $2^3=2\times 2\times 2=\frac{2^4}{2}{2}^2=2\times =\frac{2^3}{2}{s}^1=2=\frac{2^2}{2}so,2^{\circ }=1=\frac{2^1}{2}{2}^{-1}=\frac{2^{\circ }}{2}=\frac{1}{2}{2}^{-2}=\frac{2^{-1}}{2}=\frac{1}{2\times 2}{2}^{-3}=\frac{2^{-2}}{3}=\frac{1}{2\times 2\times 2}\therefore a^m=a\times a\times a\dots m\times a^{-m}=\frac{1}{a\times a\times a\times \dots m\times }$