Exponential Algebra

[Rispetto]

So here's a quick break down;

Want to go to college - computer programming.
Need grade 12 college mathematics credit, even though I have my diploma.
Worked for a little over a year, decided to go back to school.
Took an adult learning centre course (I didn't know this is what I wanted to do in HS so I was not prepared).
Put in class with drop-outs and wiggers, yada yada yada.
Anyways it's been awhile since I've needed to use my damn brain.
You're expected to know this stuff off the hop in gr 12 math, obviously.
I think I got everything down pat, I just need to verify I'm doing the right stuff.
So here I am.
I'll be posting the questions and answers I have for a couple of equations to see if I'm doing it properly. Any feedback is appreciated.
Edit: I just realized (after reading this) I forgot to swap denominator and numerator with fractions given a negative exponent. Ignore all the wrong answers (or just swap the two at the answer for the perceived correct one)

// For the first few questions I wrote everything out as the booklet instructed. I start to skip this step as I go along seeing as how it is tedious and unneeded.

1) 8^2 = 8x8 = 64

2) 4^-1 = (-1/4)

3) -3^4 = -81

4) -(2/3)^-2 = -(2/3)[-(2/3)] = (4/9) // Does the denominator stay the same(?)

5) 2x^0 = 2(1) = 1

6) (-3)^5 = -243

7) 3^-4 = (1/3)(1/3)(1/3)(1/3) = (1/81)

8) (3/4)^2 = (3/4)(3/4) = (9/16)

9) 5^0 = 1

10) 36^(1/2) = 2√36 = 6

11) 64^(1/3) = 3√64 = 4

12) (16/81)^(1/4) = 4√(16/81) = (2/81)

13) (25/144)^-(1/2) = 2√-(25/144) = -(5/144)

14) 64^(1/2) = 2√64 = 8


// And that's the first page.

15) (8)(8)^2 = 8^3

16) a^-5 b^6 c^-2 / b^8 c^7 = a^-5 b^-2 c^-9

17) (5y^3)(y^2)(5y^4) = 5 x 1 (y^3+y^2) = 5y^5 x 5y^4 = 5x5 (y^5+y^4) = 25y^9

18) (p^-2)(p^3)(p^0) = p^-2 + p^3 = p^1 + p^0 = p

19) (xyz)(x^2 y^2 z^2) = x^3 y^3 z^3

20) x^3 y^4 / x^2 y^2 = (x)y^2

21) 18x^8 y^5 / 6x^6 y^3 = (3x^2) y^2

22) x^-4 b^7 / x^11 b^-8 = x^-15 b^15

23) (y^-8) (y^-4) = y^-12

24) (a^3)^2 = a^6

// The booklet was missing 25)

26) (x^-2 y^-8)^-3 = x^6 y^24

27) (3a^2 b^3 / c^4)^(1/5)
= 3a [^2 x ^(1/5)] = 3a^(2/5)
= b [^3 x ^(1/5)] = b^(3/5)
= c [^4 x ^(1/5)] = c^(4/5)
= [3a^(2/5) b^(3/5) / c^(4/5)]

And I'll stop there.
I did this and another 3 pages, with the next 3 being the most crammed (18 questions per page).
So I hope I'm doing this right.

Edit: Also my work has come to a hault at this one;
seeing as how my booklet only teaches me how to evaluate exponential division equations with a same base number.
A lot of questions after this one pertain to the same rules of operation.

 

[NhazUl]

You got some of these wrong.

1) 8^2 = 8x8 = 64

2) 4^-1 = (-1/4)

3) -3^4 = -81

4) -(2/3)^-2 = -(2/3)[-(2/3)] = (4/9) // Does the denominator stay the same(?) -(2/3)^-2 = 1/(-(2/3)^2) = 1/(4/9) = 9/4 = 2.25

5) 2x^0 = 2(1) = 1

6) (-3)^5 = -243

7) 3^-4 = (1/3)(1/3)(1/3) = (1/27) 3^-4 = 1/(3^4) = 1/81

8) (3/4)^2 = (3/4)(3/4) = (9/16)

9) 5^0 = 1

10) 36^(1/2) = 2√36 = 6

11) 64^(1/3) = 3√64 = 4

12) (16/81)^(1/4) = 4√(16/81) = (2/81) (16/81)^(1/4) = 4√(16/81) = 2/3

13) (25/144)^-(1/2) = 2√-(25/144) = -(5/144) (25/144)^-(1/2) = √(25/144) = 5/12

14) 64^(1/2) = √64 = 8


// And that's the first page.

15) (8)(8)^2 = 8^3

16) a^-5 b^6 c^-2 / b^8 c^7 = a^-5 b^-2 c^-9

17) (5y^3)(y^2)(5y^4) = 5 x 1 (y^3+y^2) = 5y^5 x 5y^4 = 5x5 (y^5+y^4) = 25y^9

18) (p^-2)(p^3)(p^0) = p^-2 x p^3 = p^1 + p^0 = p

19) (xyz)(x^2 y^2 z^2) = x^3 y^3 z^3

20) x^3 y^4 / x^2 y^2 = (x)y^2

21) 18x^8 y^5 / 6x^6 y^3 = (3x^2) y^2

22) x^-4 b^7 / x^11 b^-8 = x^-15 b^15

23) (y^-8) (y^-4) = y^-12

24) (a^3)^2 = a^6

// The booklet was missing 25)

26) (x^-2 y^-8)^-3 = x^6 y^24

27) (3a^2 b^3 / c^4)^(1/5)
= 3a [^2 x ^(1/5)] = 3a^(2/5)
= b [^3 x ^(1/5)] = b^(3/5)
= c [^4 x ^(1/5)] = c^(4/5)
= [3a^(2/5) b^(3/5) / c^(4/5)]

 

[Rispetto]

You got some of these wrong.

Ty.

4) -(2/3)^-2 = -(2/3)[-(2/3)] = (4/9) // Does the denominator stay the same(?) -(2/3)^-2 = 1/(-(2/3)^2) = 1/(4/9) = 9/4 = 2.25

I checked and your answer is correct, but how did you get a 1 in front of the -2/3? I didn't think that applied here.

7) 3^-4 = (1/3)(1/3)(1/3) = (1/27) 3^-4 = 1/(3^4) = 1/81

Yes I actually realized my mistake on that one and edited my post, lol.

12) (16/81)^(1/4) = 4√(16/81) = (2/81) (16/81)^(1/4) = 4√(16/81) = 2/3

Forgot to use brackets on my calculator, on √(16/81). Ty.

13) (25/144)^-(1/2) = 2√-(25/144) = -(5/144) (25/144)^-(1/2) = √(25/144) = 5/12

How did you devise √(25/144) from (25/144)^-(1/2)?

18) (p^-2)(p^3)(p^0) = p^-2 x p^3 = p^1 + p^0 = p

Typo translating off paper to on-screen.

Edit: There's also something else I'm forgetting how to do.. as stated in the first post:

1 / 10^-2 is somehow 100, but I don't know how to achieve the answer.

Edit2: nvm.. 1/10^-2 = 10/1^2 = 100/1 = 100

Lol just had to look at it for a second.

 

[Dr Super Good]

I do not see fourier series nor differential equations... where is the problem?

 

[Magtheridon96]

I don't see what's the problem either.
This is very basic math : |

 

[Rispetto]

There is no problem, I just wanted someone to review the first bit of math of I've done in over a year lol.
Learning centre teachers are too busy for one-on-one work, they simply mark results.
For the first bit she didn't even tell us anything other than "get it done", seeing as how it's an 11/12 split class, and she's too busy to focus on certain stuff.
I've done all of this before, with ease, it's just a matter of remembering.
D/w about it though, NhazUl was kind enough to do it for me ;D

 

[Magtheridon96]

D/w about it though, NhazUl was kind enough to do it for me ;D

Yeah, he sucks
He stole the fun
Do you have any idea how fun solving these is? :O

 

[Rispetto]

I've got another 5 pages of solved questions so far, if you want to review them lol.
I have an answers page, but my problem before was going about getting the answer.
Typing it all into a calculator is not the idea here.