## Exponents laws and rules and how to apply these rules.

When exponents that share the same base are multiplied, the exponents are added. When an exponent is negative, the negative sign is removed by reciprocating the base and raising it to the positive exponent. ... When exponents are raised to another exponent, the exponents are multiplied.

The exponent formula is:

*a *^{n} = *a*×*a*×*...*×*a*

n times

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

For example:

2^{5} = 2×2×2×2×2 = 32

##### Multiplying exponents

*a*^{n} ⋅ *a*^{m} = *a*^{n+m}

Example: 2^{3} ⋅ 2^{4} = 2^{(3+4)} = 2^{7} = 128

*a*^{n} ⋅ *b*^{n}^{} = (*a* ⋅ *b*) ^{n}

Example: 3^{2} ⋅ 4^{2} = (3⋅4)^{2} = 12^{2} = 144

##### Dividing exponents

*a*^{n} / *a*^{m} = *a*^{n-m}

Example: 2^{5} / 2^{3} = 2^{(5-3)} = 2^{2} = 4

*a*^{n} / *b*^{n} ^{}= (*a* / *b*) ^{n}

Example: 8^{2} / 2^{2} = (8/2^{)2} = 4^{2} = 16

##### Power of exponent

(*a*^{n})^{m} = *a*^{n⋅m}

Example: (2^{3})^{4} = 2^{(3 ⋅ 4)} = 2^{12} = 4096

##### Radical of exponent

^{m}√(*a*^{n}) = *a*^{n/m}

Example: ^{2}√(2^{6}) = 2^{(6 / 2)} = 2^{3} = 8

##### Negative exponent

*a* ^{-n} = 1 / *a* ^{n}

Example: 2^{-3} = 1 / 2^{3} = 1 / 8 = 0.125

##### Zero exponent

*a* ^{0} = 1

Example: 4^{0} = 1

## What is an exponent?

Exponentiation is a mathematical operation, written as an, involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times.