# If #27sqrt(3)=sqrt(3)xx3^k#, what is #k#?

##### 3 Answers

Jan 19, 2017

Write each value in the expression as a power of three, and you will see the answer is

#### Explanation:

Since

Cancel both

Jan 19, 2017

#### Explanation:

Note that

#3^k = (27color(red)(cancel(color(black)(sqrt(3)))))/color(red)(cancel(color(black)(sqrt(3)))) = 27 = 3^3#

Hence

Jan 19, 2017

#### Explanation:

i.e.

And thus

If this were not a perfect cube, we could take