Simplify

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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 -

    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 -

    oops, the answer is 9, not ∛9
    9 is in fact ∛729

  • Simplify -

    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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