Math Help - rational expontent problem

1. rational expontent problem

the problem is as follows:

write the expression in simplest form

2/(81^(1/6))

can you explain step by step how to do this?

the answer is supposed to be:

2(3^(1/3)) / 3

i posted this somwhere else too but i wasnt getting a reply quickly enough sorry

2. Originally Posted by talhaguy
the problem is as follows:

write the expression in simplest form

2/(81^(1/6))

can you explain step by step how to do this?

the answer is supposed to be:

2(3^(1/3)) / 3

i posted this somwhere else too but i wasnt getting a reply quickly enough sorry
2 / [81^(1/6)]
= 2 / [(3^4)^(1/6)]
= 2 / [3^(4/6)]
= 2 / [3^(2/3)]
Now rationalize the denominator,
Multiply both numerator and denominatoe by 3^(1/3),
= [2 *3^(1/3)] / [3^(2/3) *3^(1/3)]
= [2 *3^(1/3)] / [3^(2/3 +1/3)]
= [2 *3^(1/3)] / [3^(3/3)]
= [2 *3^(1/3)] / [3^(1)]
= [2 *3^(1/3)] / 3 ------------answer
or,

3. Don't make double posts it wastes moderators and helpers time, and
confuses everybody.

RonL

4. Hello, talhaguy!

Write the expression in simplest form: . $\frac{2}{81^{\frac{1}{6}}}$

The answer is: . $\frac{2\cdot3^{\frac{1}{3}}}{3}$

This is identical to ticbol's solution . . . written in LaTeX.

. . $\frac{2}{81^{16}} \;=\;\frac{2}{\left(3^4\right)^{\frac{1}{6}}} \;=\;\frac{2}{3^{\frac{4}{6}}} \;=\;\frac{2}{3^{\frac{2}{3}}}$

Rationalize: . $\frac{2}{3^{\frac{2}{3}}}\cdot\frac{3^{\frac{1}{3} }} {3^{\frac{1}{3}}} \;=\;\boxed{\frac{2\cdot3^{\frac{1}{3}}}{3}}$