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1.6 Miles/hr

3 / (4 + 6n)

one trillion  =  1,000,000,000,000

300 million  =           300,000,000

one trillion / 300 million  =  10 000 / 3

It will be either 3.49 or 3.50; since the third decimal digit is a 4, round down to  3.49.

It's often easier to solve an equation if it has no denominators.  Multiply both sides by 5:

5(5)  =  5(-5 + y/5)

25  =  -25 + y

y  =  50

Distance = Rate x Time

6.4 miles  =  Rate x 4 hours                              Divide both sides by 4 hours:

6.4 miles / 4 hours  =  rate

1.6 miles / hour  =  rate

The line above the  3y - 4x  does matter; it indicates that the  3y - 4x  is to be considered as one group; it means the same thing as if they put parentheses around the  3y - 4x. Putting square parentheses around the 3y - 4x, we get:

5x - [-3x - (-2y + 5x) - (10x - [3y - 4x] ) ] 

Work from the inside parentheses out:                      simplifying the   - [3y - 4x]:

5x - [-3x - (-2y + 5x) - (10x - 3y + 4x) ]                  simplifying the  10x - 3y + 4x:

5x - [-3x - (-2y + 5x) - (14x - 3y) ]                          simplifying the   - (-2y + 5x):

5x - [-3x + 2y - 5x - (14x - 3y) ]                              simplifying the   - (14x - 3y):

5x - [-3x + 2y - 5x -  14x + 3y ]                               simplifying the  -22x + 5y:

5x - [-22x + 5y] 

5x + 22x - 5y

27x - 5y

Suggestion:  factor the numerator; since its last term is positive while the middle term is negative, its factors                        must be (a -   )(a -   )

                   factpr the denominator; since its last term is negative, its factors must be (a +   )(a -   )

                   then cancel like factors.

If you have trouble with the factoring, then post back.

If you meant:  (625a²b - 125ab²) / 25a²b²:

Factor the numerator; a common factor is  125ab:     125ab(5a - b) / 25a²b²

Cancel:  5(5a - b) / ab

It is easier to solve an equation if it has no denominators, the denominator, b, can be eliminated by multiplying each term by 'b', resulting in:

16 - 5b = 3 - 2

16 - 5b = 1                      Subtracting 16:

   -5b = -15                    Now, divide by -5.

A negative exponent on a number or variable in a fraction can be turned into a positive exponent if you move the factor from the numerator to the denominator (or from the denominator to the numerator).

For instance:  y^-3  can be written as  1 / y^3                                (this places the y³ in the numerator)         and  1 / x^-2  can be written as  x^2 / 1  , or simply as x²               (this places the x² in the denominator)   so the problem can be written (with positive exponents only) as:

(5·x²·x²·z) / (y³·y)   =   5x^4z / y^4

thx a lot :)

Because you are given possible answers, you don't really have to solve the problem; all you need to do is check the answers

The first part of the problems asks you to find the cube root of 64; it is 4 because 4x4x4 = 64. Since only one of the possible answers has 4, you're done.

If you want to simplify a cube root of a variable that has an exponent, divide that exponent by 3                                the cube root of  a^6    is  a^2                                                                                                                    the cube root of  b^15  is  b^5                                                                                                                    the cube root of  c^3    is  c^1  or just c

To find square roots, divide by 2; to find fouth roots, divide by 4, etc.

Fator the numerator:  2E - 4  =  2(E - 2)

Factor the denominator:  8E² - 22E + 12  =  2(4E² - 11E + 6)                                                                                Now, you will need to factor  4E² - 11E + 6  into two factors  (        )(      );                                                      the only factor that you have to try is  (E - 2)  because nothing else will cancel the factor in the                          numerator.        Factoring  4E² - 11E + 6  =  (E - 2)(4E - 3)

In factored form:  [ 2(E - 2) ] / [ 2(E - 2)(4E - 3) ]  =  1 / (4E - 3)

Divide the number by the number:  -96 / -24  =  4

Divide the w-terms:  W^4 / W^2  =  W^2                  (subtract exponents)

Divide the L-terms:  L^8 / L^6  =  L^2                      (subtract exponents)

Divide the M-terms:  M^2 / M^2  =  1                       (they cancel)

Multiply the individual parts together:  4W²L²

A mid-value can be negative:  for instance the mid-value between -6  and  2  is  ( -6 + 2 ) / 2  =  -2.

The midpoint between two points on a graph can have a negative x-value, a negative y-value, or both negative.

1 inch = 2.54 cm.

161 cm x (1 in / 2.54 cm)  =  63.4 inches 

To go from cm to inches, multiply by (1 in / 2.54 cm); or, just divide by 2.54.

To go from inches to cm, multiply by (2.54 cm / 1 in); or, just multiply by 2.54

Multiply each term of the equation by the common denominator:  RP · R1· R2  and simplify each term:

  R1 · R2  =  RP · R2  +  R1· RP

Factor out the RP from the right side:

  R1 · R2  =  RP · ( R2  +  R1 )

Divide both sides by ( R2  +  R1 ):

  RP  =  R1 · R2 / ( R2  +  R1 ) 

To simplify √8  -->  √8  =  √4 · √2  =  2√2

To simplify √(a^12)  -->  A square root is an exponent of 1/2

                √(a^12)  -->  (a^12)^(1/2)  =  a^6          (multiply exponents when you have a power to a power)

Putting this together:  3 · 2√2 · a^6   =  6√2 · a^6

If the problem is:  F1   =   C1 · F2 / (C1 + C2)

Cross-multiply:     F1 · (C1 + C2)   =   C1 · F2

Distribute:            F1 · C1  +  F1 · C2   =    C1 · F2

Since you are solving for C1 get all the C1 terms to one side; subtract F1 · C1 from both sides:

                          F1 · C2   =    C1 · F2  -  F1 · C1

On the right side, factor out the C1 factor:

                        F1 · C2   =    C1 · ( F2  -  F1 )

Divide by F2  -  F1:     C1  =  F1 · C2 / ( F2  -  F1 )

If you are going to solve for  b  then you want to eliminate the  a  term.

If you multiply the second equation by  -3:   (multiply each term by  -3)

     3a - 4b  =  17

    -3a - 9b  =  9

--------------------                 Add down the columns:

         -13b  =  26                 Finish:

              b  =  -2 

A negative exponent means that that factor is in the wrong place in the faction; if it is in the numerator (with a negative exponent), it belongs in the denominator; for example:  3x^-5  =  3 / x^5.

5 · x^-11 · y^2 · z^-5                 (The 5 and the y-terms have positive exponents so they stay on top;                                                                 the x and z-terms have negative exponents so they move down.)

=  5 · y^2 / ( x^11 · z^5 )

I would rearrange them so that the same letter is in the same column:

 14a  - 10b  + 5

-10a + 12b  - 7

   4a +   3b + 10

-------------------     Now, add down the columns:

   8a + 5b + 8

[ (32·x^5·z^10) ]^(1/5)  =  [ (2^5·x^5·z^10) ]^(1/5)

Since it's a power to a power, multiply the exponents together:  

[ 2 ^ ( 5 · 1/5) ] · [ x ^ ( 5 · 1/5) ] · [ z ^ (10 · 1/5) ]  

=  2^1 · x^1 · z^2

=  2xz²