Exponentiation

Exponentiation is mathematical operation to find the product of a number multiply by itself n times . Exponentiation is the inverse of Radical

${\displaystyle a^{n}=a\times a\times ...\times a}$

a to the power of n is the product of a times itself n time.

Integer Power

Power of zero	${\displaystyle a^{0}=1}$
Power of positive integer	${\displaystyle a^{n}=a\times a\times ...a}$
Power of negative integer	${\displaystyle a^{-n}={\frac {1}{a\times a\times ...a}}={\frac {1}{a^{n}}}}$

Fraction Power

Power of positive fraction	${\displaystyle a^{\frac {1}{n}}=n{\sqrt {a}}}$
Power of positive fraction	${\displaystyle a^{\frac {m}{n}}=n{\sqrt {a^{m}}}}$

Product and quotient of 2 powers

Product of 2 power	${\displaystyle a^{m}\times a^{n}=a^{m+n}}$
Quotient of 2 power	${\displaystyle {\frac {a^{m}}{a^{n}}}=a^{m-n}}$

Power of

Power of a product	${\displaystyle (ab)^{n}=a^{n}b^{n}}$
Power of a quotient	${\displaystyle ({\frac {a}{b}})^{n}={\frac {a^{n}}{b^{n}}}}$
Power of a sum	${\displaystyle (a+b)^{n}=(a+b)\times (a+b)\times ..(a+b)=}$ ${\displaystyle (a+b)^{0}=1}$ ${\displaystyle (a+b)^{1}=a+b}$ ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$ ${\displaystyle (a+b)^{3}=a^{3}+3a^{2}b+3a^{3}b^{2}+b^{3}}$
Power of a difference	${\displaystyle (a-b)^{n}=(a-b)\times (a-b)\times ..(a-b)=}$ ${\displaystyle (a-b)^{0}=1}$ ${\displaystyle (a-b)^{1}=a-b}$ ${\displaystyle (a-b)^{2}=a^{2}-2ab+b^{2}}$ ${\displaystyle (a-b)^{3}=a^{3}-3a^{2}b-3a^{3}b^{2}+b^{3}}$
Power of a power	${\displaystyle (a^{n})^{n}=a^{n}\times ^{n}}$ (n times n)

Further reading

•  Exponentiation