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# 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 xa, 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, xa is the product of multiplying a bases:  Multiplication : xa . xb = x a + b  Add exponent
Example : 33 * 34 = 33+4 = 37

Division : xa / xb = xa – b  Subtract exponent
Example : x7 / x5 = x7-5 =x2

Power of power : (xa)b = xab Multiply exponent
Example : (52)3 = 52*3 = 56

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

Power of fraction : (x/y)a = xa / ya

• Inverse : x-a = 1 / xa

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
• X1/n = n√a
• xm/n = n√am

### 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.