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

3 Answers
Shiva Prakash M V
Mar 3, 2018

#(-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)#

Niranjan
Mar 3, 2018

-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
Barney V.
Mar 3, 2018

#-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)#

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