# Please describe two laws of exponents and provide an example illustrating each law. Explain how to simplify your expression.

mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted on

Here are some of laws of exponent.

Any number or variable raised to 1 is equal to the number or variable itself.

`x^1 = x`

Example:  `5^1 = 5`

Any number or variable raised to 0 is equal to 1.

`x^0 = 1`

Example: `3^0 = 1`

Negative exponent means fraction.

`x^-1 = 1/x`

Example: `4^-1 = 1/4`

`x^-n = 1/x^n`

Example: `5^-2 = 1/5^2 = 1/25`

You can try the link below for an image of the other rules...

Sources:

crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

There are several laws of exponenets:

`x^mx^n=x^(m+n)`

When dividing exponents, subtract them:

`x^m/x^n=x^(m-n)`

When raising an exponent to another exponent, multiply them:

`(x^m)^n=x^(mn)`

Here is an example that uses all three rules:

`(x^4/x^2)^2x^4`

First, multiply the exponents raised to another exponent:

`x^((4)(2))/x^((2)(2))x^4=x^8/x^4x^4`

Next, subtract the divided exponents:

`x^(8-4)x^4=x^4x^4`