exponent-power-radicals

Learn Exponent with Examples

What is Exponent?

The base n raised to the power of a is equal to the multiplication of n, a times:

na = n × n × … × n (a times)

There:

  • “n” is the base and
  • “a” is the exponent

or

An exponent refers to the number of times a number is multiplied by itself.

An example of exponent

3 to the 4th, written as 34 means:

\dpi{120} \fn_jvn \large 3\times3\times3\times3\times = 81

 

34 is not equal to 34 = 12

Special Cases
  1. Exponent is 0:

n0 = 1

When the exponent is zero, as in 50, the result is always equal to 1.

50 = 1

26,9810 = 1

2.Exponent is negative

n-a = 1 / na

When an exponent is a negative integer, the result will always be a fraction. Fractions contain a numerator and a denominator. In this case, the numerator is always 1. To calculate the denominator, assume that the negative exponent is positive, and raise the number to that power, like this:

5-4 = 1 / 54

Some Important Rules for Exponents

Product rule with the same base

na.nb = na+b

Example:

45 . 46 = 4 5+6 = 4 11 = 4194304

Product rule with the same exponent

na . ma = (n.m)a

Example:

  1. 26. 36 = (23)6 = 66 = 36

 

Quotient rule with the same base

na / nb = na-b

Example:

46 / 45 = 46-5 = 41 = 4

 

Quotient rule with the same exponent

na / ma = (n/m)a

Example:

106 / 56 = (10/5)6 = 26 = 64

 

Power rules #1

(na)b = na.b

Example

(32)3 = 32*3 = 36 = 729

Power rule 2

exponent-math

Example

 = 4 (2^3) = 48 = 6561

Power rule with radicals

exponent-power-rule

Example

exponent-power-radicals