Describe how to transform the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent

Question

inkyvoyd · Answer

I could probably go a few more steps, but I believe you can take it from here :)

anonymous · Answer

Wouldn't it be x radical 20/3 ? Could it be simplified more?

inkyvoyd · Answer

I got the fifth power of x actually...
where are you getting the radicals from?

anonymous · Answer

$$\sqrt[3]{x ^{4}}^{5}$$

inkyvoyd · Answer

Sigh.

inkyvoyd · Answer

Yup, you're right. :)
think I read the problem wrong, and proceeded to type a huge jumbo mess in Tex >.<

inkyvoyd · Answer

though to describe the process you'd just have to do it step by step

anonymous · Answer

Okay. Could you help with one more?

inkyvoyd · Answer

sure, I guess

anonymous · Answer

I would do the same steps to simplify $$\left( \sqrt[3]{x}\right)^12$$

inkyvoyd · Answer

is that a one half or a 12?

anonymous · Answer

12 I couldn't get the 2 small.

inkyvoyd · Answer

okay, well yeah, you would just rewrite as
$\Huge (x^\frac{1}{3})^{12}=x^{\frac{1}{3}*12}$

inkyvoyd · Answer

also, you may know this already, but a common mistake is to think that $\Huge x^{(a^b)}=(x^a)^b$. The two are entirely different statements, though.

anonymous · Answer

Im so confused now. :(

inkyvoyd · Answer

starting where?

anonymous · Answer

Would it be x radical 4 then?

inkyvoyd · Answer

x to the power of 4 actually

anonymous · Answer

So what does radical  mean?

inkyvoyd · Answer

a radical is an nth root. it's basically a square root sign you see, but instead with cube root (denoted with a small three), or a fourth root, or in general any nth root where n is a positive integer.

anonymous · Answer

Oh okay! Well thanks for all the help! Really appreciate it!

inkyvoyd · Answer

no problem - let me know if you need any more help!