/* 
Laura Toma
csci 107

Write a recursive method exp that raises a positive (> 0) integer to a
non-negative (>= 0) power; i.e. exp(3,2) should return 9.  To do this,
it helps to think about exponentiation recursively.  If we want to
raise m to the n power, we can think as follows:


m^n  = 1          if n = 0
m^n = m x m^(n-1) if n>0

Suggested test inputs (correct answer after arrow): 

exp (3,2) ==> 9
exp(83,0) ==> 1
exp(124, 1)==> 124
exp(1,124) ==> 1
exp(5,4) ==> 625
exp(10,3) ==> 1000


*/  

#include <iostream.h>


/* compute recursively and return a^b */
int exp(int a, int b) {

  if (b<0) {
    cout << "sorry. only positive exponents" << endl;
    return 0; 
  }
  
  //a^0 = 1
  if (b==0) {
    return 1; 
  }

  //else ..a^b = a * a^(b-1)
  return a * exp(a, b-1); 
}

int main() {

  int m, n; 
  cout << "enter m="; 
  cin >> m; 
  cout << "enter n="; 
  cin >> n;
  cout << "m^n = " << exp(m,n) << endl;
  return 0;
}