# Math 10 Week 3

This week we learned about exponents. I was was having trouble simplifying equations with negative exponents. We ended up going over negative exponents and how to deal with them. You need to make sure you leave all the exponential answers in positive form and to do so you need to…

Vocab: Multiplication Law – Add the exponents when they have the same base. Ex. $5^6\cdot5^2$ = $5^8$

Division Law – Subtract the exponents when they have the same base. Ex. $\frac{5^6}{5^2}$$5^4$

Integral (Negative) Exponent Law – Place the coefficient with the negative exponent on the other side of the division line to make the exponent become positive.

Work

1. Find all the hidden exponents.
2. Place all the coefficients with negative exponents on the other side of the divide line and then the exponents will become positive.
3. Use the multiplication Law
4. Use the Division Law
5. Come the two parts
6. If needed use another Exponent Law.

See Below for Pictures 🙂

# Math 10 Week 2

This week I struggled with being positive. I wasn’t quite understanding how to convert mixed radicals to simplest form when it has an exponent of 3 or 4. I was getting very frustrated and thought I was going to fail the numbers test. I ended up going in after school and received help from a friend. I now understand it and i’m able to explain it to others.

Ex. $3\sqrt[3]{162}$

Vocab:

Radical – The radical is the number under the line Ex. $\sqrt{162}$

Coefficient – The Coefficient is the Larger number on the outside Ex.  $3\sqrt{162}$

Index – The index is the little number on the outside. Ex. $3\sqrt[4]{162}$

How to convert the mixed radical into simplest form you need to:

1. Find all the prime factors from the radical, using a factor tree or a factor table.
2. Bring the coefficient over to the radical side. *** Any time that you are bringing in something from the outside in, the index should always come with it. There will be two now. One on the outside and one on the inside. (When it is attached to a number it is called an exponent).
3.  Break down the $3^4$ into its full form.
4. Circle any groups of 4 that you see.
5. One Group of four  = One of that number. Two groups = Two of the number.
6. Bring the two 3s outside.
7. Multiply the 3s together
8. You now have the simplest form of $3\sqrt[4]{162}$

See below for pictures

# Math 10 Week 1

This week I learned how to find the Lowest Common Multiple of 2 or more numbers. This is something I struggled with earlier this week. While doing my homework, I compared my answers with the real ones and when I got something wrong I retraced my steps and fixed any errors.

To find the Lowest Common Multiple of: Ex. 12, 30, and 105

1. Create a factor tree or factor table.
2. Sort the prime numbers from lowest to highest for 12, 30 and 105
3. make into exponents.
4. sort into groups- Notice that there is sometimes a prime number that is not a prime factor of another number. In this case you need to make that prime number to the power of 0 in the group that does not have that prime factor. Ex. 2 is a prime factor of 12 and 30 but not of 105. you need to write it like this- 12= 2 to the power of 2, 30= 2 to the power of 1 and, 105= 2 to the power of 0.
5. You have now sorted into groups 🙂
6. Chose the highest exponent from each group.
7. Multiply the numbers you have chosen
8. You should be left with the LCM of 12, 30 and 105. Good Job!

See below for pictures