Exponent Rules

We are used to simplifying 2x + 3x = 5x, but sometimes it's not that simple.

If you have something like 2x²y + 3x²y = 5x²y it is not always as obvious as to why it's the same.

Basically, if you have the same variables to the same exponent, they are considered like terms and can be added using normal addition rules.



 $\left(x^a\right)^b=x^{a\cdot b}$  

ex.)  $\left(2a^2\right)^{3\ }=\ 2^3a^{\left(2\cdot3\right)}=8a^6$  

 $x^{-a}=\frac{1}{x^a}$  

ex.)  $4z^{-3}=\frac{4}{z^3}$  

Look out for whole numbers. They don't move unless they  have an exponent next to them.

 $x^0=1$  

ex.)  $8y^0=8\left(1\right)=8$  

Look out for whole numbers. They don't change unless the 0 exponent is directly affecting them.