Question

Express each of the following as a rational number of the form $\frac{p}{q}$,where p and q are integers and $q\ne 0:\left(i\right)2^{-3}\left(ii\right)(-4{)}^{-2}(iii\left)\frac{1}{3^{-2}}\right(iv\left){\left(\frac{1}{2}\right)}^{-5}\right(iv){\left(\frac{2}{3}\right)}^{-2}$

Answer 1

$\left(i\right)2^{-3}=\frac{1}{2^3}=(\because a^{-m}=\frac{1}{a^m})=\frac{1}{2\times 2\times 2}=\frac{1}{8}\left(ii\right)(-4{)}^2=\frac{1}{(-4{)}^2}=\frac{1}{(-4)\times (-4)}=\frac{1}{16}(iii)\frac{1}{3^{-2}}=3^2(\frac{1}{a^{-m}}=a^m)=3\times 3=9(iv){\left(\frac{1}{2}\right)}^{-5}={\left(\frac{2}{1}\right)}^5=2\times 2\times 2\times 2\times 2=32(v){\left(\frac{2}{3}\right)}^{-2}={\left(\frac{3}{2}\right)}^2=\frac{3}{2}\times \frac{3}{2}=\frac{9}{4}$