How do you simplify #(2\root[ 3] { 49} ) ( 5\root [ 3] { 7} )#?

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Answer 1 · 2017-10-15T15:08:34

70

Given,# [2 root(3)49][5 root(3)7]#

#rArr [2. (49)^(1/3)][5. 7^(1/3)]#

#rArr 2. 5. (7^2)^(1/3). 7^(1/3)#

#rArr 10. 7^(2/3).7^(1/3)# [ As #(a^m)^n = a^(mn)]#

#rArr 10. 7^(2/3+1/3)# [ As #a^m. a^n = a^(m+n)]#

#rArr 10. 7^[(2+1)/3]#

#rArr 10. 7^(3/3)#

#rArr 10. 7^1#

#rArr 10. 7 # [ As #a^1 = a#]

#rArr 70#