fractional exponents BaSH/bc extention

#!/bin/bash
scale=$1;
echo ${scale:="20"} >> /dev/null;
echo "number to raise:";read y;
echo "numerator of exponent:";read n;
echo "denominator of exponent:";read d;
x=1;prev=0; #//x = guess;prev = loop control testing;
for((z=0;z<50;)) do
x=$(echo "scale=$scale;$x*(1-1/$d)+$y/$d/$x^($d - 1)"|bc); #//see newton method for finding the Nth root of a number.
if [[ "$x" == "$prev" ]]; then z=555; fi;
prev=$x;
if [[ $(echo $2|head -c 2) == "-d" ]]; then echo $prev; fi;
done;
echo;echo -n "$y^($n/$d)="; echo "$x^$n"|bc;