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