## anonymous 5 years ago simplify 8^2/3 x 2^-1/3

1. anonymous

$8=2^{3} so... 8^{(2/3)}=2^{2}$

2. anonymous

then you have 2^2 * 2^(-1/3). Add the exponents

3. anonymous

$8^{\frac{2}{3}}$ means cube root of 8 squared. cube root of 8 is 2, 2 squared is 4

4. anonymous

2 + (-1/3) = 5/3 So the answer would be 2 ^ (5/3)

5. anonymous

i got lost somewhere

6. anonymous

in order to simplify, you have to have a common base. So by simplifying the 8, you can get everything written with a base of 2

7. anonymous

8. anonymous

like satellite said, the cube root of 8 is 2, so that gives you 2^2

9. anonymous

well, when multiplying, you add the exponents....think x^2*x^3 = x^5

10. anonymous

i understand the first number, not the second 2^(-1/3)

11. anonymous

so, since they both have a base of 2, you can add their exponents

12. anonymous

13. anonymous

You don't have to change anything in 2^(-1/3), since it alrady has a base of 2

14. anonymous

how do you get 5/3 by adding -1/3 and 2

15. anonymous

sorry im slow lol

16. anonymous

get common denominators....2 = 6/3

17. anonymous

:)

18. anonymous

-1/3 + 6/3 = 5/3

19. anonymous

duh moment lol

20. anonymous

haha

21. anonymous

makes sense now

22. anonymous

great!

23. anonymous

im new to this site. how exactly does it work...students helping students?

24. anonymous

mostly

25. anonymous

i have a few more of these problems, but i want to try them myself...try at least lol

26. anonymous