(-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