1. ## exponents

Problem:
(2^9/2^8 * sixth root of 3)^4

We have to solve it labeling each step.

I have it down to

(2^1 * sixth root of 3)^4 by the quotient of powers

I am stuck from there, though.

2. (2^9/2^8 * sixth root of 3)^4

You are getting closer.

2^9/2^8 = 2^1 or more commonly known as 2.

because 2^(9-8) = 2^1

sixth root of three can be written as 3^(1/6)

so.

[ 2*3^(1/6) ]^4
Apply the 4 to inside the bracket

2^4 * 3^[ (1/6)*4) ]

16 * 3^(4/6)
16 * 3^(2/3)
=33.281341

3. Thank you, Darlin!

4. Hey there lmschneider,

It's a bit hard to establish what your question looked like from the notation, but taking it literally...

(2^9/2^8 * sixth root of 3)^4 is $\displaystyle (\frac {2^9}{2^8} * \sqrt[6]{3}) ^4$

If this is the case...

$\displaystyle (\frac {2^9}{2^8} * \sqrt[6]{3}) ^4 = (2 \sqrt[6]{3})^4$

$\displaystyle = (2 * 3^{\frac{1}{6}})^4$

$\displaystyle = (2^4 * 3^{\frac{4}{6}})$

$\displaystyle = 2^4 * 3^{\frac{2}{3}}$

$\displaystyle = 16 * \sqrt[3]{3^2}$

$\displaystyle = 16 \sqrt[3]{9}$

Trust this helps...

5. Thank you!