Question

What is 9^1/3 times 81^1/3 simplified

Answer 1

use exponential propoerties to make your life easier

remember

`(x^m)^n=x^(mn)`
and

`x^(m)/(n)=\sqrt[n]{x^m}`
and

`(x^m)(x^n)=x^(m+n)`


so

write everybody as base 3


`9=3^2`

`81=9^2=(3^2)^2=3^4`



`(9^(1)/(3))(81^(1)/(3))=`

`((3^2)^(1)/(3))((3^4)^(1)/(3))=`

`(3^(2)/(3))(3^(4)/(3))=`

`3^(2+4)/(3)=`

`3^(6){3}=`

`3^2=`

`9`