Question

@AccessDenied

Answer 1

I would start by combining the powers into a single power, and simplify the fraction.
\( \left( 3^{2/3} \right)^{1/6} \)
We just multiply the powers together. And it seems that 2 and the 6 can be simplified a little. :)

Answer 2

i dont know how /.\

Answer 3

You know this rule about exponents?
\( \left( a^b \right)^c = a^{b \times c} \)
In our case, a = 3, b = 2/3, and c = 1/6.
\( \left( 3^{2/3} \right)^{1/6} = 3^{\color{blue}{(2/3) \times (1/6)}} \)
So focus on the exponent:
\( \color{blue}{\dfrac{2}{3} \times \dfrac{1}{6}} \)
In fractions, you just multiply straight across, right?

Answer 4

i guess lol so

Answer 5

would it simplify as 1/3 ?

Answer 6

It won't make much sense unless it is clear! :p
\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a\times c}{b \times d} \)

\( \dfrac{2}{3} \times \dfrac{1}{6} = \dfrac{2 \times 1}{3 \times 6} \)

Answer 7

Not quite, there would actually be two 3's in the denominator multiplied together, so 1/9.
\( \dfrac{\cancel{2}}{3 \times (\cancel{2} \times 3 )} = \dfrac{1}{9}\)

Answer 8

okay cx

Answer 9

is it B ?

Answer 10

So the last step is just converting back to the radical, which does end up being B.
\( \displaystyle 3^{1/9} = \sqrt[9]{3} \)