Posted by Brady on Friday, February 14, 2014 at 6:32pm.
Simplify the following number.
∛729
I think it is ∛9, but I do not know. Please help, and check my answer. I will appreciate it if you guys can answer this as soon as possible. It is part of a RATIONAL EXPONENTS question.
The original equation was 9^(1/3)∙〖81〗^(1/3). Once I turned both into square roots, I multiplied them, and I got ∛729, which I think simplifies to ∛9. Also, please again answer and check my answer, and answer as soon as possible. I will appreciate it if you do.

Simplify  Steve, Friday, February 14, 2014 at 6:35pm
since 729 = 9^3, you are correct.
Your method was also correct.
81 = 9^2, so
81^(1/3) = (9^2)^(1/3) = 9^(2/3)
and
9^(1/3) * 9^(2/3) = 9^(3/3) = 9
fractional exponents are just like any others. Add them when multiplying, and multiply them when raising powers to powers.

Simplify  correction  Steve, Friday, February 14, 2014 at 6:36pm
oops, the answer is 9, not ∛9
9 is in fact ∛729

Simplify  Brady, Friday, February 14, 2014 at 6:41pm
Thank you, I just wasn't sure if it needed to be simplified more, or I needed to do it again by doing another way. So, everything leads to 9, I'll remember that.
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