Grade 9 Math Help: Simplifying Radical Expressions

[Talonkabayama]

Homework Statement

(∜(∛(√625) ) )^6

Homework Equations

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

The Attempt at a Solution

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

 

[Mark44]

Homework Statement

(∜(∛(√625) ) )^6

Homework Equations

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

The Attempt at a Solution

(∜(∛(√625) ) )^6
= (√(8&625))^6

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.

= √(48&625)

 

[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

 

[eumyang]

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).

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

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*

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?

 

[SammyS]

Do you understand how to express radicals as fractional powers?

 

[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*

 

[HallsofIvy]

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

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).)

 

[NascentOxygen]

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