EXPONENTIATION

Exponentiation is a mathematical operation, written as b^{n}, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n"; when n is a positive integer, exponentiation corresponds to repeated multiplication of the base, b^{n} is the product of multiplying n bases.

b^{n} is called "b raised to the nth power", "b raised to the power of n", "the nth power of b", "b to the nth power", or most briefly as "b to the nth".

b^{1} = b

b^{0} = 1

b^{-1} = 1/b, the reciprocal of b

b^{-n} = 1/b^{n}

b^{n}⋅b^{m} = b^{n+m}

b^{n}/b^{m} = b^{n-m}

b^{n}⋅a^{n} = (b⋅a)^{n}

b^{n}/a^{n} = (b/a)^{n}

(^{n}√b)^{n} = b

b^{1/n} = ^{n}√b

(b^{1/n})^{n} = b^{(1/n)⋅n} = b^{1} = b

b^{n/m} = ^{m}√b^{n}

e^{x}-e = e(e^{x}/e-e/e) = e(e^{x-1}-1)

(a+b)^{c/d} = a^{c/d}(1+b/a)^{c/d}