# Thread: A problem with fractional indices

1. ## A problem with fractional indices

I have tried everything I know, but I can't solve this. Can you please show me the right direction?

$\frac{16^\frac{1}{3}*4^\frac{1}{3}}{8}$

Thank you!

2. Originally Posted by Coach
I have tried everything I know, but I can't solve this. Can you please show me the right direction?

$\frac{16^\frac{1}{3}*4^\frac{1}{3}}{8}$
change everything to base 2

$\frac {16^{\frac {1}{3}} \cdot 4^{\frac {1}{3}}}{8} = \frac { \left( 2^{4} \right)^{\frac {1}{3}} \cdot \left( 2^{2} \right)^{\frac {1}{3}}}{2^3}$

Now continue

3. Thank you so much!

But I would still have another question

$\frac{x^{2n+1}*x^\frac{1}{2}}{\sqrt{x^{3n}}}$

Thank you!

4. Originally Posted by Coach
Thank you so much!

But I would still have another question

$\frac{x^{2n+1}*x^\frac{1}{2}}{\sqrt{x^{3n}}}$
change the square root in the denominator to a power (you know how to do that, right? see my post here)

so we get $\frac{x^{2n+1}*x^\frac{1}{2}}{\sqrt{x^{3n}}} = \frac{x^{2n+1}*x^\frac{1}{2}}{x^\frac {3n}{2}}$

Now continue

5. ok, so is it like

$x^{2n+1+\frac{1}{2}}-^{\frac{3n}{2}}$ ?

6. Originally Posted by Coach
ok, so is it like

$x^{2n+1+\frac{1}{2}}-^{\frac{3n}{2}}$ ?
yes