simplify 8^2/3 x 2^-1/3

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simplify 8^2/3 x 2^-1/3

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[8=2^{3} so... 8^{(2/3)}=2^{2}\]
then you have 2^2 * 2^(-1/3). Add the exponents
\[8^{\frac{2}{3}}\] means cube root of 8 squared. cube root of 8 is 2, 2 squared is 4

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Other answers:

2 + (-1/3) = 5/3 So the answer would be 2 ^ (5/3)
i got lost somewhere
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
they are added...not multiplied?
like satellite said, the cube root of 8 is 2, so that gives you 2^2
well, when multiplying, you add the exponents....think x^2*x^3 = x^5
i understand the first number, not the second 2^(-1/3)
so, since they both have a base of 2, you can add their exponents
ok...gotcha on the addition
You don't have to change anything in 2^(-1/3), since it alrady has a base of 2
how do you get 5/3 by adding -1/3 and 2
sorry im slow lol
get common denominators....2 = 6/3
:)
-1/3 + 6/3 = 5/3
duh moment lol
haha
makes sense now
great!
im new to this site. how exactly does it work...students helping students?
mostly
i have a few more of these problems, but i want to try them myself...try at least lol
thanks for your help

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