1. anonymous

$6\sqrt{2*6\sqrt{8\div6\sqrt[3]{?2}}}$

2. anonymous

exponential equations? can anyone explain in English?

3. anonymous

I'm not sure what the ? means so I'm going to ignore it. What you can do is set that whole expression equal to some value a. Square both sides. Then square them again. Then cube both sides. Now all the radicals are gone and you will have integer exponents on both sides. you should have a^12 on the right. Take the whole thing on the left and raise it to the 1/12 power. That is the value of the expression.

4. anonymous

i can help you with the steps if you need. Is this what you wanted; a simplified expression?

5. anonymous

simplify

6. anonymous

allright did my post make sense to you?

7. anonymous

not really. I have no Idea what I'm doing

8. anonymous

ok ill try to type it in the equation editor.

9. anonymous

k

10. anonymous

$6\sqrt{2*6\sqrt{8\div \sqrt[3]{2}}}=a$ square both sides $36*2*6\sqrt{8\div6\sqrt[3]{2}}=a ^{2}$ square both sides again $36^{2}*2^{2}*6^{2}*8\div6\sqrt[3]{2}=a ^{4}$ cube both sides $36^{6}*2^{6}*6^{6}*8^{3}/(6^{3}*2)=a^{12}$

11. anonymous

now just take everything to the 1/12 power

12. anonymous

and you've simplified to just one rational exponent

13. anonymous

ok?

14. anonymous

i kind of get it

15. anonymous

you can simplify it even further than i said by subtracting exponents

16. anonymous

k

17. anonymous

I have trouble with the exponents

18. anonymous

do you know x^a/x^b=x^(a-b)

19. anonymous

no

20. anonymous

if you have two exponential terms with the same base when you multiply them you can add the exponents and when you divide you can subtract the exponents

21. anonymous

ok

22. anonymous

x^a*x^b=x^(a+b)

23. anonymous

$\left(6\sqrt{2*6\sqrt{\frac{8}{6\sqrt[3]{2}}}}\right)^2\text{->}\left(144\ 2^{5/6} \sqrt{3}\right)^2\text{->}124416\ 2^{2/3}$$\sqrt[4]{124416\ 2^{2/3}}= 12\ 2^{5/12} 3^{1/4}$

24. anonymous

Took the original problem expression and deleted the ? mark. Squared the expression and simplified. Squared the result and simplified. Took the fourth root of the last expression to offset the two squares and simplified. Would never attempt this thing without Mathematica executing the book keeping so to speak.

25. anonymous

robtobey and my answers are equivalent

26. anonymous

Think i'll go talk to my teacher tomorrow. I don't understand it. Thank for your help though

27. anonymous

depends on what you think is simplest i geuss though. Allright good luck

28. anonymous

To verify the result, Mathematica reported "True" regarding the assertion that the following expression was valid:$6\sqrt{2*6\sqrt{\frac{8}{6\sqrt[3]{2}}}}\text{=}12\ 2^{5/12} 3^{1/4}$