Question

Find to five places of decimals the value of :
$(630{)}^{-\frac{3}{4}}$

Answer 1

let

$y=(625+5{)}^{\frac{-3}{4}}=\frac{1}{125}(1+.004{)}^{\frac{-3}{4}}$

$=\frac{1}{125}[1+(.004)\left(\frac{-3}{4}\right)+\left(\frac{.000016}{2!}\right)\left(\frac{21}{16}\right)+....]$

let us neglect the term as well

$=.008[1-.003]$

$=.007976$