Which expression is equal to 4mn^8/28m^5n^3 ? n^5/7m^4n^5/7m^57m^5/n^47n^5/m^4

(-4mn)284(m2n3)/28m4n5(mn)2/28(m2n2)5/(4m2n3)2  

Final result :

 2560m298n298  

 ————————————

      49      

Step by step solution :

Step  1  :

Equation at the end of step  1  :

                 ((m2)•(n3))              ((mn)2)  (((m2)•(n2))5)

 -4mn)284)•———————————)•(m4))•(n5))•———————)•——————————————

                     28                     28     ((22m2•(n3))2)

Step  2  :

           m10n10

Simplify   ——————

           24m4n6

Dividing exponential expressions :

2.1    m10 divided by m4 = m(10 - 4) = m6

Dividing exponential expressions :

2.2    n10 divided by n6 = n(10 - 6) = n4

Equation at the end of step  2  :

                 ((m2)•(n3))              ((mn)2)  m6n4

 -4mn)284)•———————————)•(m4))•(n5))•———————)•————

                     28                     28      16  

Step  3  :

           m2n2

Simplify   ————

            28  

Equation at the end of step  3  :

                 ((m2)•(n3))              m2n2  m6n4

 -4mn)284)•———————————)•(m4))•(n5))•————)•————

                     28                    28    16  

Step  4  :

           m2n3

Simplify   ————

            28  

Equation at the end of step  4  :

                 m2n3          m2n2  m6n4

 -4mn)284)•————)•m4)•n5)•————)•————

                  28            28    16  

Step  5  :

5.1   Negative number raised to an even power is positive  

For example let's look at (-7)6 , where (-7) , a negative number, is raised to 6 , an even exponent :

(-7)6 can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)6 can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 76 which is positive.

We proved that (-7)6 is equal to (7)6 which is a positive number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

5.2     4 = 22 (-4)284 = (22)284 = 2568

Equation at the end of step  5  :

                    m2n3                m2n2    m6n4

 2568m284n284 • ————) • m4) • n5) • ————) • ————

                     28                  28      16  

Step  6  :

Multiplying exponential expressions :

6.1    m284 multiplied by m2 = m(284 + 2) = m286

Multiplying exponential expressions :

6.2    n284 multiplied by n3 = n(284 + 3) = n287

Dividing exponents :

6.3    2568   divided by   22   = 2(568 - 2) = 2566

Equation at the end of step  6  :

    2566m286n287                m2n2    m6n4

 (((———————————— • m4) • n5) • ————) • ————

         7                      28      16  

Step  7  :

Multiplying exponential expressions :

7.1    m286 multiplied by m4 = m(286 + 4) = m290

Equation at the end of step  7  :

   2566m290n287          m2n2    m6n4

 ((———————————— • n5) • ————) • ————

        7                28      16  

Step  8  :

Multiplying exponential expressions :

8.1    n287 multiplied by n5 = n(287 + 5) = n292

Equation at the end of step  8  :

  2566m290n292    m2n2    m6n4

 (———————————— • ————) • ————

       7          28      16  

Step  9  :

Multiplying exponential expressions :

9.1    m290 multiplied by m2 = m(290 + 2) = m292

Multiplying exponential expressions :

9.2    n292 multiplied by n2 = n(292 + 2) = n294

Dividing exponents :

9.3    2566   divided by   22   = 2(566 - 2) = 2564

Equation at the end of step  9  :

 2564m292n294    m6n4

 ———————————— • ————

      49         16  

Step  10  :

Multiplying exponential expressions :

10.1    m292 multiplied by m6 = m(292 + 6) = m298

Multiplying exponential expressions :

10.2    n294 multiplied by n4 = n(294 + 4) = n298

Dividing exponents :

10.3    2564   divided by   24   = 2(564 - 4) = 2560

Final result :

 2560m298n298  

 ————————————

      49      

the correct answer is d

hope this