# The Power with Natural Exponent

Suppose, we have a is the real numbers, and n is natural numbers equals more than one; n-th power of the number a are product of n multipliers, each of them equal a, i.e.

The number a is the base of exponent, n is the power of exponent.

If n=1 , then will suppose a^1=a.

For example, (1/3)^4=1/3*1/3*1/3*1/3=1/81 .

The following properties are correct:

1. a^n*a^k=a^(n+k)
2. a^n-:a^k=a^(n-k),if n>k
3. (a^n)^k=a^(nk)
4. a^n*b^n=(ab)^n
5. a^n/b^n=(a/b)^n, b!=0

For example, 2^3*2^5=2^(3+5)=2^8 ;

(2^3)^5=2^(3xx5)=2^15 ;

(2/5)^3=2^3/5^3=8/125 .