## anonymous one year ago please help Which of the following is equal to square root of the cube root of 2? 2 to the power of 2 over 3 2 to the power of 3 over 2 2 to the power of 1 over 3 2 to the power of 1 over 6

1. welshfella

|dw:1437238306035:dw|

2. anonymous

wait so what answer choice would that be?

3. welshfella

thats just an example - the above would be the 4th root of x cubed

4. welshfella

another example might be |dw:1437238633165:dw|

5. welshfella

that would be the 4th root of the cube root of x

6. welshfella

(as 1/12 = 1/4 * 1/3)

7. welshfella

you question is of the last type

8. anonymous

so would it be the 3rd answer choice?

9. welshfella

no

10. welshfella

2 to the power of 1 over 3 is just the cube root

11. anonymous

oh... im so confused, could you explain how i would solve mine? |dw:1437238875011:dw|

12. welshfella

|dw:1437238926440:dw|

13. anonymous

i think i see how you got that

14. welshfella

|dw:1437238989772:dw|

15. anonymous

oh! so would it be...|dw:1437239064652:dw|?

16. welshfella

yep

17. anonymous

thank you!

18. welshfella

yw

19. anonymous

can you help me with one more?

20. welshfella

i only have 5 minutes but ok

21. anonymous

|dw:1437239179722:dw| sorry if the drawings confusing

22. welshfella

|dw:1437239236820:dw|

23. welshfella

= 2^(1/2 + 1/3)

24. welshfella

25. anonymous

|dw:1437239307901:dw|

26. welshfella

- no - you have multiplied 1/2 * 1/3 in this case you add them law of exponents x^a * x^b = x^(a+b)

27. welshfella

1/2 + 1/3 = 3/6 + 2/6 = ?

28. anonymous

so...|dw:1437239543505:dw|

29. welshfella

- no iv shown you how to add them in my last post

30. welshfella

gotta go

31. anonymous

ohhh i got it thank you so much

32. anonymous

$\sqrt{\sqrt[3]{2}}=\sqrt{2^{\frac{ 1 }{ 3 }}}=(2^{\frac{ 1 }{ 3 }})^\frac{ 1 }{ 2 }=2^{\frac{ 1 }{ 3 }\times \frac{ 1 }{ 2 }}=2^{\frac{ 1 }{ 6 }}$