How to properly write rational exponents when expressed as roots?
I'm aware that we can express $x^{2/3}$ as $(x^2)^{1/3} = (x^{1/3})^2$. Expressing these exponents in terms of roots is something that confuses me. Should the above expression be written as:
$$(\sqrt[3]{x})^2 \quad \text{or} \quad \sqrt[3]{x^2}$$ and what difference does it make if we write it in one way or the other?
Note: I'd also appreciate it if you could answer this question more generally and also refer to the domains of functions you mention (e.g. $\sqrt{x}$, so $x \geq 0$) in your answer.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
649
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 870 views
- $4.50
Related Questions
- Algebra Question
- How do we take the mean of a mathematical function using statistics?
- Generating set for finitely generated submodule of finitely generated module
- Guywire, finding height of the powerpole
- real analysis
- A word problem about a rectangular carpet
- Rank, Range, Critical Values, Preimage, and Integral of Differential Forms
- Sigma-Algebra Generated by Unitary Subsets and Its Measurable Functions