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 be viewed only if
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
Aman R
643
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 440 views
- $4.50
Related Questions
- How do you prove that when you expand a binomial like $(a+b)^n$ the coefficients can be calculated by going to the n row in Pascal's triangle?
- Compounding interest of principal P, where a compounding withdrawal amount W get withdrawn from P before each compounding of P.
- Measure Theory and the Hahn Decomposition Theorem
- Rank, Range, Critical Values, Preimage, and Integral of Differential Forms
- Linear Algebra - Matrices (Multiple Choice Question) (1st Year College)
- Variance of Autoregressive models, AR(1)
- Prove that a closed subset of a compact set is compact.
- Representation theory 2 questions