Question

write in exponential form-
(a)262.144 (b)-625/256 (c)3125/16807

Answer 1

$$\begin{gathered} \left(\mathbf{a}\right)\mathbf{.} \\ 262.144 \\ =\frac{262144}{1000} \\ =\frac{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}{2\times 2\times 2\times 5\times 5\times 5} \\ =\frac{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}{5\times 5\times 5} \\ =\frac{2^{15}}{5^3}=\frac{{\left(2^5\right)}^3}{5^3}={\left(\frac{32}{5}\right)}^3 \\ \left(\mathbf{b}\right)\mathbf{.} \\ \frac{-625}{256}=\left(-1\right)\times \frac{5\times 5\times 5\times 5}{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}=-{\left(\frac{5}{4}\right)}^4 \\ \mathrm{Similarly}\mathrm{you}\mathrm{can}\mathrm{solve}\mathrm{the}\mathrm{remaining}\mathrm{part}. \end{gathered}$$