Power

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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:

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Expansion of a to the power n 

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

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