It is given that \(\mathrm{h}(x)=\dfrac1{\sqrt[3]{8-3x}}\).
Find the binomial expansion for \(\mathrm{h}(x)\), in ascending powers of \(x\), up to and including the term in \(x^2\). Give the coefficients as exact fractions in their simplest form.
State the range of values of \(x\) for which the expansion is valid.[4]
By putting \(x=\dfrac1{16}\) into the expansion in (a)(i), find an approximate value of \(\sqrt[3]{16}\), as a fraction in its lowest terms, in the form \(\dfrac ab\), where \(a\) and \(b\) are integers.[3]