Powers with integer exponent

Summary

• $a^n$ : $a$ is the base, $n$ is the exponent , $a∈R,n∈Z$ :
• If $n∈N$ ( $n$ is a natural number) then $a^n$ is defined as

$$a^n=a⋅a⋅…⋅a$$

• ( $n$ factors)
• If $n∈N$ then $-n<0$ and $-n∈Z$ . If $a≠0$ then $a^{-n}$ is defined as

$$a^{-n}= \frac{1}{a^n}= \frac{1}{a⋅a⋅…⋅a}$$

• ( $n$ factors)
• $a^0=1$ if $a≠0$ (else undefined)
• $0^b=0$ if $b>0$ (else undefined)
• Exponentiation before multiplication/division so $2⋅3^2=2⋅9$ and not $6^2$ .
• ${a^n}^m$ means $a^{\left( n^m \right)}$ . If you want to raise $a^n$ to the power $m$ , write ${\left( a^n \right)}^m$