This week in math 10 we went over greatest common factors (GCF), least common multiples (LCM), prime factorization and the exponent laws. While I found all of these different concepts interesting to learn about, I believe the most important thing I learned were the exponent laws. I believe that the exponents laws were the most important concept I learned this past week because as I start to do more advanced work  not understanding the basic exponent laws will make more complicated equations much more difficult to do.

 

There are four different exponent laws:

The Multiplication Law of Exponents:

When the bases are the same, the exponents can be added together.

Ex: x^6 + x^4                  6+4=10

=x^10

The Division Law of Exponents:

When the bases are the same, the exponents can be subtracted together.

Ex: x^11 ÷ x^5                 11-5=6

=x^6

The Power of a Power Law:

When an exponent/base are inside of a bracket and another exponent is on the left side of the bracket simply multiply the exponents together.

Ex: (x^5)^3                    5×3=15

=x^15

The Zero Exponent Law:

When the exponent is 0, the base becomes 1.

Ex: x^0

=x^1

 

Combining the Exponent Laws:

When combining the exponent laws it is important to not mix up the individual exponent rules within the equation.