1. Sep 28, 2011

### Talonkabayama

1. The problem statement, all variables and given/known data

(∜(∛(√625) ) )^6

2. Relevant equations

I'm not sure, I haven't done math for the whole summer ( visited Europe, etc)

3. The attempt at a solution

(∜(∛(√625) ) )^6
= (√(8&625))^6
= √(48&625)

2. Sep 28, 2011

### Staff: Mentor

What does 8&625 mean?
What happened to the two outer radicals?
I can't even guess what you did here.

Write all radicals as fractional exponents, and go from there.

3. Sep 28, 2011

### Talonkabayama

ummmm &= super scirpt (my computer just does that) and I though that if I
took (∜∛√625)^6
added the powers (4+3+1) then multiplied by the exponent outside the brackets (8×6) and got the product 48. so √(48&625).
I'm really unsure of what to do my teacher gave me this because she was impressed with my abilities insofar as our curriculum. I have no I dea how to accomplish this though. I've been trying to use exponent laws (product, quotient, power-of-a-power rules)

oh so like.. ummm I can't do super script so can *= superscript then when I'm done with it an additional * (i.e. 5*2*=25) and for fractional exponents can 1/4 work?
( 625*1/4*x625*1/3*x625)*6*

I don't know if I've made this more complicated then necessary but I'm really stressed from all my projects

Last edited: Sep 28, 2011
4. Sep 28, 2011

### eumyang

That doesn't work that way. The 4, 3, and 1 (where did you get 1?) are not exponents.

This is closer. But don't repeat the base. Use the properties of exponents. And by the way, a square root = exponent of 1/2.
$\left(\sqrt[4]{\sqrt[3]{\sqrt{625}}}\right)^6$
$= \left(\sqrt[4]{\sqrt[3]{(625)^{1/2}}}\right)^6$
Can you take it from here?

5. Sep 28, 2011

### SammyS

Staff Emeritus
Do you understand how to express radicals as fractional powers?

6. Sep 29, 2011

### Talonkabayama

ummm do you multiply the fractional exponents?
like
1/4 x 1/3 x 1/2
=1/24 so like 624 to the power of 1/24th

(625 *1/24*) *6*

7. Sep 29, 2011

### HallsofIvy

Staff Emeritus
You seem to be just doing things pretty much at random. If you are not sure, look them up in your text book.

Some rules you need to know:
$\sqrt[n]{a}= a^{1/n}$.
$(a^m)^n= a^{mn}$

Yes, $\sqrt[4]{\sqrt[3]{\sqrt{625}}}= (((625)^{1/2})^{1/3})^{1/4}= (625)^{1/24}$.
(Not "624" as you have once.)

And now, what is $(625^{1/24})^6$. (Do NOT try to find $625^{1/24}$!) (It would have been sufficient to note that (1/4)(1/3)(1/2)= (1/4)(1/6).)

8. Oct 1, 2011

### Staff: Mentor

Why not work it out on your calculator first, then you'll know what answer you need to get when doing it using theory.