How do you simplify #\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }#?

1 Answer
Mar 28, 2018

Answer:

#7/(root(5)(4)a^(2/5)b^(13/5))#

Explanation:

First, we take the root of each product

#\frac { 7a } { \root[ 5] { 4a ^ { 7} b ^ { 13} } }=(7a)/(root(5)(4)root(5)(a^7)root(5)(b^13))#

#root(a)(b^c)=b^(c/a)#

#(7a)/(root(5)(4)root(5)(a^7)root(5)(b^13))=(7a)/(root(5)(4)a^(7/5)b^(13/5))#

#(a^b)/a^c=a^(b-c)#
#a=a^1#

#(7a)/(root(5)(4)a^(7/5)b^(13/5))=7/(root(5)(4)a^(2/5)b^(13/5))#