Mgccl's blogI'm the standard deviAsian.

echo bcpow(3, 1/3);//out put 1, also, input should be string
//but it is automatically converted from number to string
echo pow(3, 1/3);//out put 1.44224957

//BCMath equivalent of pow(6, 4.5)
bcmul(bcpow(6,4),bcsqrt(6));
//BCMath equivalent of pow(6, 3.25)
bcmul(bcpow(6,3),bcsqrt(bcsqrt(6));

function bcgetscale(){
	return strlen(bcadd(1,0))-2;
}

//Version 0.1 of BCRoot
//To do: Optimize the speed by use as much bcsqrt as possible.
function bcroot($a, $n, $scale='default'){
	$default = bcgetscale();//Get the scale
	if($scale == 'default'){
		$scale = $default;//use default scale
	}
	if($n & ($n-1)){//check if $n is the power of 2, return 0 if is
       //now use Newton's method to find the number
		bcscale($scale+15);
		$x = 1;
		$k = 0;
		$limit = ceil(log($scale+15)/log(2))+1;
		while($k<$limit){
			$t1 = bcdiv(1,$n);
			$t21 = bcmul(bcsub($n,1),$x);
			$t22 = bcdiv($a,bcpow($x, $n-1));
			$t2 = bcadd($t21,$t22);
			$x = bcmul($t1, $t2);
			++$k;
		}
		bcscale($default);
		return bcadd($x,0,$scale);
	}else{
    //here use many bcsqrt, because this is FAST
		$i = 0;
		$pow = log($n)/log(2);
		while($i < $pow){
			$a = bcsqrt($a,$scale);
			++$i;
		}
		return $a;
	}
}

//BCMath + BCExt equivalent of pow(6, 2/3)
bcmul(bcpow(6,2),bcroot(6,3));