Posted by Brady on .
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,
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,
oops, the answer is 9, not ∛9
9 is in fact ∛729 
Simplify 
Brady,
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.