Idea is to use two java threads, one thread calculates base1 ^ power1 using BigInteger and another thread calculates base2 ^ power2. Use thread.join() to wait for both thread to complete and sum result from both thread.

package com.dw.thread;

import java.math.BigInteger;

public class ComplexCalculation {

    public BigInteger calculateResult(BigInteger base1, BigInteger power1, BigInteger base2, BigInteger power2) throws InterruptedException {
        BigInteger result;
        /*
            Calculate result = ( base1 ^ power1 ) + (base2 ^ power2).
            Where each calculation in (..) is calculated on a different thread
        */

        PowerCalculatingThread thread1 = new PowerCalculatingThread(base1, power1);
        PowerCalculatingThread thread2 = new PowerCalculatingThread(base2, power2);

        thread1.start();
        thread2.start();

        thread1.join();   // important: wait thread to complete
        thread2.join();  
        result = thread1.getResult().add(thread2.getResult()); // add two result

        return result;
    }

    private static class PowerCalculatingThread extends Thread {
        private BigInteger result = BigInteger.ONE;
        private BigInteger base;
        private BigInteger power;

        public PowerCalculatingThread(BigInteger base, BigInteger power) {
            this.base = base;
            this.power = power;
        }

        @Override
        public void run() {
           /*
           Implement the calculation of result = base ^ power
           */
            for (BigInteger i = BigInteger.ZERO; i.compareTo(power) != 0; i = i.add(BigInteger.ONE)) {
                result = result.multiply(base);
            }
        }

        public BigInteger getResult() { return result; }
    }
    public static void main(String[] args) throws InterruptedException {
        ComplexCalculation c = new ComplexCalculation();
        BigInteger result = c.calculateResult(new BigInteger("123"), new BigInteger("10"), new BigInteger("456"), new BigInteger("20"));

        System.out.println(result);
    }
}