function claculate(str) {
    let numbersStack = [];
    let operatorsStack = [];
    let operators = {
        '+' : {
            order : 1,
            func : (r,l) => {return l+r;}
        },
        '-' : {
            order : 1,
            func : (r,l) => {return l-r;}
        },
        '*' : {
            order : 2,
            func : (r,l) => {return l*r;}
        },
        '/' : {
            order : 2,
            func : (r,l) => {return l/r;}
        },
        '^' : {
            order : 3,
            func : (r,l) => {return Math.pow(r,l);}
        },
        '(' : {
            order: 0
        }
    }

    for (let i=0; i<str.length; ++i) {
        if (str[i] === ' ') continue;

        // read the numbers
        if (!isNaN(str[i])) {
            let tmp = "";
            // more then single digit
            while (!isNaN(str[i])) {
                tmp += str[i++];
            }
            numbersStack.push(parseInt(tmp));
        }

        if (str[i] === '(') {
            operatorsStack.push(str[i]);
        } else if (str[i] === ')') {
            // calculate the expression in the parentheses
            while (operatorsStack[operatorsStack.length - 1] !== '(') {
                numbersStack.push(operators[operatorsStack.pop()].func(numbersStack.pop(),numbersStack.pop()));
            }
            operatorsStack.pop();
        } else if (Object.keys(operators).indexOf(str[i]) !== -1) {
            // keep the order of execution
            while (operatorsStack.length !== 0 && operators[operatorsStack[operatorsStack.length - 1]].order >= operators[str[i]].order) {
                numbersStack.push(operators[operatorsStack.pop()].func(numbersStack.pop(),numbersStack.pop()));
            }
            operatorsStack.push(str[i]);
        }
    }

    // calculate remaining operators
    while(operatorsStack.length !== 0) {
        numbersStack.push(operators[operatorsStack.pop()].func(numbersStack.pop(),numbersStack.pop()));
    }

    // last remaning element is the result
    return numbersStack.pop();
}

console.log(claculate("2+4")) // 6
console.log(claculate("1+2 * 3")) // 7
console.log(claculate("2 * (3 - 1)^4")) // 32