This week I finished the unit Exponents, Radicals, and Scientific Notation and, with it, the entire course Pre-algebra.

For the most part I found understanding exponents not to be too difficult. It turned out I still had a good understanding of exponents from high school. Things I learned/re-learned included:

1. It’s helpful to imagine you’re always multiplying 1 at the beginning of an exponent (ex. 2^2 = 1 x 2 x 2). This is make 2^0 make more sense. (2^0 = 1 x _ = 1. The _ space doesn’t equal 0 but rather used to show that you’re not multiplying 1 by anything and therefor are left with 1).
2. A negative number to an odd power will equal a negative number and a negative number to an even power will equal a positive number (ex. (-1)^1 = -1 and (-1)^2 = 1).
3. 0^0 and 0^1 are considered Undefined.
4. When the base numbers in an exponent equation are the same (ex. 6 in 6^3 + 6^5) you can add the exponents together (ex. 6^3 + 6^5 = 6^3+5 = 6^8)
5. When two numbers are multiplied or divided inside a bracket with an exponent outside of it, both numbers will be subjected to the exponent (ex. (4*5)^3 = (4^3) * (5^3)).
6. When there are two exponents separated by a bracket, you can multiple the exponents (ex. (2^3)^4 = 2^3*4 = 2^12)
7. A number to a negative power/exponent is the same as 1 over that number to the positive exponent (ex. 4^-3 = ¼^3).

I also worked on evaluating square roots, cube roots and radicals. I practiced taking the square roots out of radicals by using prime factorization. I also worked on converting numbers into scientific notation, and multiplying/dividing scientific notation numbers by each other. I wrote out a guide that I found helpful:

1. 10^0 = 1
2. 10^1 = 10
3. 10^2 = 100
4. 10^3 = 1, 000 (1 thousand)
5. 10^4 = 10, 000
6. 10^5 = 100, 000
7. 10^6 = 1, 000, 000 (1 million)
8. 10^7 = 10, 000, 000
9. 10^8 = 100, 000, 000
10. 10^9 = 1, 000, 000, 000 (1 billion)
11. 10^10 = 10, 000, 000, 000
12. 10^11 = 100, 000, 000, 000
13. 10^12 = 1, 000, 000, 000, 000 (1 trillion)

I think it’s worth remembering 3, 6, 9, and 12 are 1 thousand, 1 million, 1 billion, and 1 trillion respectively. For me, remembering this makes it easier to quickly think of the value of a number written in scientific notation even if it’s one below or above 3, 6, 9, and 12 (if 10^6 = 1 million then 10^5 = 1 hundred-thousand.

I did the Unit test twice and on the second time through I was perfect up until the final question. I did it too quickly and got it wrong. I was pretty mad but I didn’t bother to redo it to get 100%. I did, however, get 100% on the course challenge on my first try which I was quite pleased about considering it had been a few weeks since doing some of the type of questions at the beginning of the Pre-algebra course.

I’m nervous but excited to be moving on to the Algebra course. I’m nervous because I think I’ll finally be starting to get into math that I didn’t learn in high school and therefore have no recollection of it that I’ll be able to draw from. I’m worried that I’ll find it too difficult and won’t be able to understand it. There’s also a part of me that says “I don’t give a shit how hard this is, I’m going to keep working through it until I understand it.” There’s also part of me that thinks I’m probably smarter than I give myself credit for. That’s the part of me that’s excited to get started.