## anonymous 5 years ago Can someone explain how to solve $3^{-1/3}\times27^{-1/2}$ Thanks! :)

1. Mohsen

$3^{-1/3}\times3^{3(-1/2)}$ $3^{-1/3+(-3/2)}$ $3^{-1/3-3/2}$ $3^{(-2-9)/6}$ $3^{-11/6}$

2. anonymous

how do you simplify that further? :D

3. Mohsen

$27=3^{3}$ then solve the fraction...

4. Mohsen

$a ^{m} \times a ^{n}=a ^{m+n}$ the base must equal...

5. anonymous

i mean, how do you simplify $3^{-11/6}$ further? because actually, i got that answer too. but the answer isn't in the choices given. thanks!

6. Mohsen

what the choices?

7. anonymous

$\sqrt[6]{3}$ $\sqrt[6]{3}/9$ $3\sqrt[6]{3}/2$ and $3\sqrt[6]{3}$

8. anonymous

$3^{-\frac{11}{6}} =3^{-2}.3^{1/6}={\sqrt[6]{3} \over 9}$

9. Mohsen

the answer is $\sqrt[6]{3}/9$ $3^{-11/6}=$ $\sqrt[6]{3^{-11}}$ $\sqrt[6]{3^{1}/3^{12}}$ $\sqrt[6]{3^{1}}/\sqrt[6]{12}$ $\sqrt[6]{3}/3^{12(1/6)}$ $\sqrt[6]{3}/3^{2}$ $\sqrt[6]{3}/9$

10. anonymous

Anwara, how is 3−116=3−2.31/6 ?

11. Mohsen

wow,anwar.how do u do that?

12. anonymous

i meant, how did you get to the 2nd equation? and thanks, mohsen!

13. anonymous

Because $$-2+1/6= \frac{-12+1}{6}=-11/6$$, which is the same exponent :)

14. anonymous

@Mohsen: do what?

15. Mohsen

same question with phoebeca :) bt u answered it :) thanks

16. anonymous

You're welcome!

17. anonymous

thanks guys!

18. Mohsen

19. anonymous

i agree!

20. anonymous

Thanks mohsen :)