Math Exponentiation Formulas

Math Exponentiation Formulas

Before we you about Math Exponentiation Formulas. You should know what is Exponentiation?

What is Exponentiation?

Answer : Exponentiation is a mathematical operation. It is used as square and multiply algorithm, which is written as x^a, it is involving two numbers, the base x and the exponent a. When a is a positive integer, exponentiation corresponds to repeatedly multiplication of the base that is, x^a is the product of multiplying a bases:

Multiplication : x^a . x^b = x ^{a + b}  Add exponent
Example : 3³ * 3⁴ = 3³⁺⁴ = 3⁷

Division : x^a / x^b = x^{a – b}  Subtract exponent
Example : x⁷ / x⁵ = x^7-5 =x²

Power of power : (x^a)^b = x^ab Multiply exponent
Example : (5²)³ = 5^2*3 = 5⁶

Power of Product : (xy)^a = x^a y ^a Multiply exponent

Power of fraction : (x/y)^a = x^a / y^a

• Inverse : x^-a = 1 / x^a

1. Zero power : x⁰ = 1 (x != 0)

• Why a number raised to the 0 power is ?
  x / x = 1
  so, x / x = x¹ / x¹ = 1
  therefore, x¹ / x¹ = x ^1-1 = x⁰ = 1

• X^1/n = n√a

• x^m/n = n√a^m

If the exponent is power of 2

Example 1: Find 3¹²⁸ mod 7

So, 3² mod 7 = 9 mod 7 = 2
then, 3⁴ mod 7 = 9² mod 7 = 81 mod 7 = 4
then, 3⁸ mod 7 = 4² mod 7 = 16 mod 7 = 2
therefore, 3¹⁶ mod 7 = 2² mod 7 = 4
then, 3³² mod 7 = 4² mod 7 = 2
then, 3⁶⁴ mod 7 = 2² mod 7 = 4
therefore, 3¹²⁸ mod 7 = 4² mod 7 = 2
So, 3¹²⁸ mod 7 = 2.

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