Rules for Exponents

When multiplying numbers with expontents be sure to only multiply numbers that have the Same Base!

 For Example, if you had x^6 and X^4 you could multiply them, because they share the same base.

However if you had x^6 and y^9 you couldn't multiply them, because their because their bases are not the same.

Here are six rules to remember when working with exponents-

1. X^m x X^n=X^m+n

2. X^m/X^n=X^m-n

3. (X^m)^n=X^mn

4. X^0=1

5. X^-n= 1/X^n

6. X^m/n =n square root of x^m



How to Identify the Dimensions of a Matrix

To identify the dimensions of a matrix first count the number of rows, then the number of columns.

For example, for the above matrix you count the number of rows (they go horizontally from left to right), and there are 3. Then you count the number of columns (they go vertically from left to right) and there are also 3. Therefore you have a 3 by 3 matrix! Any matrix with the same number of rows as columns is a perfect square matrix. 

This matrix would be a 4 by 3 matrix!

 

Systems of Equations

There are three types of systems of equations.
Consistent Independent systems when graphed intersect. The point of intersection is the solution to the system. This system has only one solution.

Consistent Dependent systems when graphed have infinitely many solutions and therefore are one line directly on top of each other.

Inconsistent Systems are systems that have NO solutions! They are parallel when graphed and never intersect.