Rewrite the rational exponent as a radical expression.

(3^2/3)^1/6

Question

Rewrite the rational exponent as a radical expression.

(3^2/3)^1/6

aum · Answer

$\Huge (3^{\frac 23})^{\frac 16} = 3^{\frac 23 * \frac 16} =3^{\frac 19} = \sqrt [9]{3}$

anonymous · Answer

how did you get the denominator as 9

aum · Answer

$\Large \frac 23 \times \frac 16 = \frac {2}{18} = \frac 19$

mathmate · Answer

@danibear401
Just in case, is the question:
$\Huge (3^{\frac 23})^{\frac 16} $ or $\Huge ({\frac {3^2}{3}})^{\frac 16} $
If it's the first case, parentheses are required around "2/3" for proper interpretation.

aum · Answer

^^^ Good point.  Parenthesis required around both fractions 2/3 and 1/6 for my first reply to be valid.

In the book or online page there may not be a parenthesis because they can write "vertically" such as $\Large 3^{\frac 23}$.  But when you write "horizontally" you have tp group them together using parenthesis: 3^(2/3).  By grouping 2/3 using parenthesis, we know 3 is raised to the whole thing (2/3).  But if you write 3^2/3 it will be interpreted as $\Large \frac {3^2}{3}$.

anonymous · Answer

its the first one and thank you