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# Math Exponentiation Formulas

## Math Exponentiation Formulas

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
x / x = x1 / x1 = 1
x1 / x1 = x 1-1 = x0 = 1
1. X1/n = n√a

• xm/n = n√am

If the exponent is power of 2
Example 1: Find 3128 mod 7

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

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