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:

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

• a^m = 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, a^m x aⁿ = a^m+n

• For any a ≠ 0, and integers m, n, (a^m) ⁿ = a^mn

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