# Exponent

Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation is repeated multiplication of the base: that is, an is the product of multiplying n bases:

And  we have,

• a0 = 1
• a¹ = a
• a² = a x a
• a³ = a x a x a
• an = a x a x a …. a x a (a is multiplied n times)

Here case, an is called the n-th power of a, or a raised to the power n.

Some common exponents have their own names:

•  Exponent 2 is called the square of a (a2) or a Square
• Exponent 3 is called the cubeof a (a3) or a cubed.
• Exponent −1 of a, or 1 / a, is called the reciprocal of a.

POINTS TO REMEMBER:

• 0n = 0 for n > 0; 0n is not defined for n ≤ 0

• am = an if and only if m = n for any a ≠ 0, 1 or  -1

• For any a ≠ 0, and natural number n, a-n = 1/an

• For any a ≠ 0, and integers m, n, am x an = am+n

• For any a ≠ 0, and integers m, n, (am) n = amn

• For any a ≠ 0, b ≠ 0 and integers m, (ab)m = am x bm