Question

How do you simplify `81^sqrt2 div 3^sqrt2`?

Answer 1

`3^(3sqrt2)=27^sqrt2`

Explanation:

We can take our original:

`81^sqrt2-:3^sqrt2`

and rewrite it this way:

`(3^4)^sqrt2/3^sqrt2`

which can then be written as:

`(3^(4sqrt2))/(3^sqrt2)`

and then we can write it as:

`(3^(3sqrt2+sqrt2))/(3^sqrt2)=(3^(3sqrt2)xx3^sqrt2)/(3^sqrt2)`

cancel the two like terms and get:

`(3^(3sqrt2)xxcancel(3^sqrt2))/cancel(3^sqrt2)=3^(3sqrt2)=27^sqrt2`