HELP! I dont remember how to simplify!?

Question

I don't remember how to simplify these can anyone help me...i want the answer but i WANT YOU TO EXPLAIN how you got the answer (i have a lot of other problems that need to be simplified..i really just want to understand and get the idea of how you do it). Thank you sooo much!

x ^-3

--------

x ^-5

2x^3 y^2

-------- * ------

y ^-5 3x^7

x^2-4x-5

-------------

x^2+2x+1

x-4

-----

4-x

(x-1)^3

x^-1/3 x^-3/5

(For the last one I'm not sure if the negative sign is for the whole fraction or for just the denominator...on my paper it just comes right after the x...but the negative and the fraction are exponents)

Hopefully you understand lol...b/c i dont...

Answer 1

x ^-3

--------

x ^-5

= x^-3+5 = x^2  ------------- ( you should use the division method of       exponent  when the denominator goes up the sigh of exponent changes, here it was - and when it goes up to numerator it became plus) If we have same express, as here we have x , then we can divide.

2x^3 y^2

-------- * ------

y ^-5 3x^7

= 2x^3-7 * y^2+5

------------------------------

3

= 2x^-4*y7                  ---- ( you take the same expression together)

----------------

     3

x^2-4x-5

-------------

x^2+2x+1

= X^2-2 - 4x - 5

------------------------

2x + 1

= x^0 - 4x - 5

-------------------------

2x + 1

= -4x-5

  --------------

   2x +1

x-4

-----

4-x

= - (- x + 4)

   -------------        ( you flip the sign so that it looks like same)

     (-x+ 4)

= -1

(x-1)^3

= x3 - 1 - 3x + 3

i hope u understand it now.. and can do the rest urself ;)

Answer 2

        X^-3

       ____  

        X^-5

  From the Laws of indices, you substract the power

  Therefore   = X^-3-(-5) = X^-3 + 5 = X^2

  2 X^-3 Y^2

  ----------------

  Y^-5x 3X^7

  From the law of indices, you substract

then  2                                      2

        ----  X^-3-7 x Y^2-(-5) =   --- X^-10 Y^7

        3                                       3



   x^2-4x-5        

   -------------  

   x^2+2x+1

You find the factors of (X^2-4X-5) and (X^2+2X+1)



    x^2-4x-5          (X -5 ) (X +1)

    -------------  =    ------------------

    x^2+2x+1        (X+1) (X+1)

    X+1 council out and you get

    

                              (X-5)

                     =       -------

                              (X+1)

     x-4

     -----  you re-arrange the denominator to get

     4-x



     x-4          X-4              X - 4

     -----  =     ------    =      --------     =  -1

     4-x          -X+4           -(X - 4)

    

     (x-1)^3   =  (X-1) (X-1) (X-1)

      you expand the first two factors i.e

      (x-1)^3   =  X( X-1) -1(X-1) [(X-1)]

                    =   X^2 -X -X +1 [(X-1)]

                    =   (X^2 -2X +1) (X-1)

      expand and you get

    

                    =   X^2(X-1) -2X(X-1) +1(X-1)

                    =   X^3 - X^2 -2X^2 +2X +X -1  

      collect like terms

                    =   X^3 - 3X^2 +3X -1

       x^-1/3 x^-3/5 From the Laws of indices, you add powers

      x^-1/3 x^-3/5 = X^ (-1/3) + (-3/5)

               you find the L.C.M of 3 & 5 which is 15

    

                            =   X^ ( -5-9)/15

                            =   X^ -14/15

Answer 3

Ok, I'll try my best since I only have the slightest memory of it.

x ^-3

--------

x ^-5        I think to make the signs positive, you have to flip them.

              So it becomes:

x ^+5

--------

x ^+3

For the second one I'm not sure but I'll tell you what I did and hope it'll help.

I put y^2 on the bottom and put 3x^7 to the top. 2x^3X3x^-7

                                                                    ----------------

                                                                     y^-5Xy^-2  

Then I combined the variables on the bottom but I'm not sure to multiply them or add them.

Hope it helped a little. =)

Answer 4

Jenn : you are a top contributor .so how come this exponents solution ( surd's ) are difficult for you.

exponents  in multiplication  ADD up and in division they subtract.( having the same base )

x^-3 /X^-5 = x ^-3+5 = X^2

2x^3-7 y ^2+5 /3   2/3 x^-4y^7 ans

third  factorize the top and bottom eqns

X^2-4x-5 = x^2+x-5x- 5 =  (x+1)(x-5)

X^2+2x+1 = (x+1)(X+1)

hence  X+1)(X-5) / (x+1)(x+1) =  (x-5)/ (x+1) ans

x-4/4-x check teh 4-x  can be written as - ( x-4)

hence answer is  -1

hope now you can solve others