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

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Answer 1 · 2017-01-19T22:10:58

Write each value in the expression as a power of three, and you will see the answer is $k=3$

Since $sqrt3=3^(1/2)$ and $27=3^3$ we can write the expression as

$(3^3*3^(1/2))/3^(1/2) = 3^k$

Cancel both $3^(1/2)$ powers to get

$3^3 = 3^k$

Answer 2 · 2017-01-19T22:12:10

$k=3$

Note that $27 = 3^3$ , so we find:

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

Hence $k = 3$

Answer 3 · 2017-01-19T22:12:43

$k=3$

$(27sqrt3)/sqrt3=3^k$

i.e. $3^k=(27cancelsqrt3)/cancelsqrt3=27=3xx3xx3=3^3$

And thus $k=3$ .

If this were not a perfect cube, we could take $"logs"$ of both sides:

$klog3=3log3$

If 27sqrt(3)=sqrt(3)xx3^k27sqrt(3)=sqrt(3)xx3^k, what is kk?