[Math] the difference between radical and exponent

complex numbersexponentiationterminology

Is radical a type of exponent? What do we call the power when it is a complex number?

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A radical $x^\frac{1}{n}$ (the $n$th root of $x$) is a subset of exponents $x^y$ where $n\in\mathbb{Z}$ and $y\in\mathbb{R}$.

You can still use the terms "exponent" and "power" when $x\in\mathbb{C}$, but radicals are more ill-defined.

Related Solutions

[Math] the difference between exponentials and powers

Euler's number, $e \approx 2.71828$, is very important in many fields of mathematics. An important function that uses this constant is $\exp x = e^x$.

However, $\operatorname{pow}(a, b) = a^b$, a more general case.

You will notice that, if $a=e$,

Math.pow(Math.E, x)

is the same as

Math.exp(x)

Once you are familiar with more properties of $e^x$, you will also note that

Math.exp(b * Math.log (a))

is the same as

Math.pow(a, b)

[Math] the difference between exponent, power and index

Unfortunately, terminologies here can be confusing. I would call $n$ the "exponent". But one might speak of $b$ as "$a$ to the power $n$" (which makes it sound like $n$ is the "power"), or "the $n$'th power of $a$" (which makes it sound like $b$ is the "power").

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[Math] the difference between exponentials and powers

[Math] the difference between exponent, power and index

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