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I finally got it. Thanks a lot. Sorry it took like literally 2 or more hours lel.

What if we had this....???

3 - .2 (3)

Wouldn't this factor as

3(1-.2)  ???

Because.....distributing the 3 back across the parentheses would give us

3 - .2(3)    ....just what we started with....

So...it works the same with 10^x

10^x - .2 (10^x)  =

10^x( 1 - .2)

I don't know how to explain my problem.

I don't understand how

10^x - .2 *10^x

Transforms into 10^x(1 -.2)

The two problems I have are understand how 10^x dissappears and how the equation changes into (1-0.2)

How many people are there ?

10.25/15 = 0.68(3) ≈ 0.68

Percent means "per hundred". X percent means X/100.

So when you have a decimal that you want to convert into percentages, simply multiply by 100.

10.25/15 = 0.68(3) ≈ 0.68 = 68/100 = 68 %

We see that: 2500 = 25 * 100

We know that: √(a * b) = √a * √b

Thus: √2500 = √(25 * 100) = √25 * √100 = 5 * 10 = 50

If you add 40 to what?????

I don't understand your question.....we're just taking out the greatest common factor....just like normal Algebra

What happens exactly when you factor out 10^x.

If we're talking about

10^x -0.2 * 10^x

Factor out the 10^x

10^x(1 - .2)

Note...if we distribute the "10^x" across both terms, we have what we started with

10^x - .2*10^x

10^x - .2 *10^x *10^x

but we started with

10^x - .2 *10^x?

10^x (1 - .2 *10^x)

If I were to distribute the "10^x" over both of the terms  in the parentheses, we would have

10^x - .2 *10^x *10^x  ....just what we started with....

I was reffering to the

10^x -0.2 * 10^x

becoming just

(1 -0.2)10^x

I want to understand how this one of the 10^x disappears.

(1/8) ^-2   is the same thing as  (8/1)² = (8)² = 64

I'm not converting  10^x to 1

I'm writing 

10^x  = 100  in log form

If I take the log of both sides, we get

log10^x  = log 100        and by a log rule ....  loga^x =  x log a

So

log10^x   = x log 10.....so we have

x log 10  = log100    divide both sides by log 10

x = log 100 / log 10       but log 10 = 1    so we have

x =( log 100) / 1  = log 100  = 2

1/4 + 1/6 + 1/8 is 13/24  ???

Get a common denomnator  = 24....so we have

6/24 + 4/24 + 3/24  = 13/24

So it's true...

So basically you "convert" one 10^x to 1 because log 10 = 1 ?

Note that if we have

a^x  = b      we can write this in log form as

log b/ log a = x

So

10^x = 100

In log form, we're saying

(log 100) / (log 10) = x     but since log 10 = 1, we can just write this as

(log100) / 1   = log 100 = x   

And

log 100  = 2

the answer is 1 over 64

√π ≈ 1.7724538509055160272981674833411

Ok. I pretty much got it covered now. But can you explain the significance of 10^x. Since you're taking it of the equation. How can this be. I know you probably already explained this 100 times.

Sorry....I am trying to do too many things at once..

I meant to type

10^x *(.2)  = 20

So

10^x = 20/.2

10^x = 100

3 + 4 + 11 = 18

And since the angles sum to 180, we have

3/18 x 180  =  30 degrees

4/18 = 40 degrees

11/18 = 110 degrees

but 40/0,2 is 200?

(3/4) ^-3   is the same thing as

(4/3)³  =

64/27