Questions on Algebra: Negative and Fractional exponents answered by real tutors!

See how you like this way where we get rid of parentheses first.
I'm going to take more steps than necessary because you can do 
several of these steps all in one step:



1. We make sure every factor shows its 1 exponent if it doesn't already 
have another exponent.  Like this:



2. When you have a fraction multiplied by a non-fraction, make the
non-fraction into a fraction by putting a 1 under it:



3. Next remove the parentheses by distributing every exponent
that is inside the parentheses times the exponent just outside the
parentheses. The -4 will be squared so we can just ignore the negative
dign: 



4. There are only two negative exponents. The rule is: Move the
factors with negative exponents on the bottom to the top, and on
the top to the bottom, and change the sign of the exponent to
positive.  So we move m-20 to the bottom as m20 and we move n-2 to the top as n2.



5. Let's just have one big fraction:

   

6. Let's add the exponents of like letters in order to multiply:



7. Let's subtract the exponents larger minus smaller
and place the result where the larger exponent was
The m22 is on the bottom and the m2 is on the
top. So we subtract exponents 22-2 and get 20 and write m20 on
the bottom because the larger exponent was on the bottom.



8.  Write the 91 as 9 and then as 32



9. Subtract the exponents of 3 and get 32 on the top
because the largere exponent was on top. 



10. Write 32 as 9 and  42 as 16

 

11. Multiply the 9 by the 16 and get 144



Edwin

1 - 2ab - (a² + b²)

Remove the parentheses:

1 - 2ab - a² - b²

Enclose the last three terms in a parentheses preceded by a minus:

1 - (2ab + a² + b²)

Swap the first two terms inside the parentheses:

1 - (a² + 2ab + b²)

Factor the trinomial in the parentheses:

1 - (a + b)(a + b)

Write that as a square:

1 - (a + b)²

Factor as the difference of two squares:

1² - (a + b)²

[1 - (a + b)][1 + (a + b)]

Remove the inner parentheses:

[1 - a - b][1 + a + b]

Change the brackets to parentheses:

(1 - a - b)(1 + a + b)

Edwin