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` .