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 \({\left( a^n \right)}^m\)