Question

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

Answer 1

`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))`