Question

Express the number $\frac{1}{512}$ in the exponential form:

Answer 1

Let us factorize $512$ as follows:

$512=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=2^9$

Now,

$\frac{1}{512}=\frac{1}{2^9}=2^{-9}(\because forx\ne 0\frac{1}{x}=x^{-1})$

Hence the exponential form of the number $\frac{1}{512}$ is $2^{-9}$.