Question

How do you simplify `( - 9m ^ { \frac { 1} { 2} } n ^ { \frac { 4} { 5} } ) ( 2m ^ { \frac { 1} { 3} } n ^ { \frac { 2} { 5} } )`?

Answer 1

`(-9m^(1/2)n^(4/5))(2m^(1/3)n^(2/5))=-18m^(5/6)n^(6/5)`

Explanation:

`(-9m^(1/2)n^(4/5))(2m^(1/3)n^(2/5))=-9xx2xxm^(1/2)m^(1/3)n^(4/5)n^(2/5)`
`-9xx2=-18`
`m^(1/3)n^(4/5)=m^(1/2+1/3)=m^((3+2)/(2xx3))=m^(5/6)`
`n^(4/5)n^(2/5)=n^(4/5+2/5)=n^((4+2)/5)=n^(6/5)`

Thus,
`9xx2xxm^(1/2)m^(1/3)n^(4/5)n^(2/5)=-18m^(5/6)n^(6/5)`
Now,

`(-9m^(1/2)n^(4/5))(2m^(1/3)n^(2/5))=-18m^(5/6)n^(6/5)`

Answer 2

-18`m^(5/6)` `n^(6/5)`

Explanation:

• Multiply the like terms (constant with constant, m with m and n with n)
• Multiplying like terms means the addition of their powers. So `m^(1/2) * m^(1/3)` = `m^((1/2)+(1/3))` and `n^(4/5) * n^(2/5)` = `n^((4/5)+(2/5))`
• Also multiply the constants -9 and 2 to get the answer

Answer 3

`-18m^(5/6)n^(6/5)`

Explanation:

`(-9m^(1/2)n^(4/5))(2m^(1/3)n^(2/5))`

`:.=-18m^(1/2+1/3)n^(4/5+2/5)`

`:.=-18m^((3+2)/6)n^(6/5)`

`:.=-18m^(5/6)n^(6/5)`