# How to read multiplication, division, and power?

I heard from some video lectures, $x^2$ is $x$ squared, and $x^3$ is $x$ cubed.

Could someone let me know how to read $x^n$?

$x$ to the n?

$x$ to the n power?

$x$ to the n powered?

$x$ to the nth power?

Also, I saw an Indian professor is reading $e^x$ as both '$e$ to the $x$' and 'exponential of $x$'.

Please teach me the right expression.

Which one is right to read $y=4x$?

$y$ is equal to four times of $x$

$y$ is equal to four times $x$

$y$ is equal to four multiplying $x$

$y$ is equal to four $x$

Which one is right to read $\displaystyle y=\frac 4 x$

$y$ is equal to four over $x$

$y$ is equal to four by $x$

$y$ is equal to four divided by $x$

$y$ is equal to four dividing $x$

I am sorry for asking not mathematics but English. But I want to know the answer from mathematicians, not from people unrelated to math.

• "x to the n" and "x to the n-th power" both make sense to me for the first case, for the second case either is fine, for the third "y is equal to four times x" or "y is equal to 4x" are fine, for the last case "y is equal to four divided by x" is fine. Note that things like "to the n-th power' and "four divided by x" are more technically accurate, but the ones I highlighted are the ones that any mathematician will understand. – miradulo Sep 19 '15 at 15:59
• @ Donkey Kong Thank you very much. – Danny_Kim Sep 19 '15 at 16:02

"$x$ to the $n$-th power" or "$x$ to the power of $n$" are both correct. Some people also say "$x$ to the $n$", but I believe that this is gramatically not completely correct [though it is more practical].

$e^x$ can also be called "exponential of $x$", because the function $x \mapsto e^x$ is called exponential function.

The equation $y = 4x$ can be pronunced either "$y$ equals four $x$" or "$y$ is equal to four times $x$" [and combinations of these two].

The term $\frac{4}{x}$ is pronunced "$4$ divided by $x$".

• Thank you, can I ask one more thing? I've heard 'two by four, and two over four' before. by and over are wrong? Actually, in my country, read denominator first, and then say numerator. So very confused T.T – Danny_Kim Sep 19 '15 at 16:06
• I've never heard "2 by 4", but it might be a correct pronounciation. "2 over 4" is the binomial coefficient $\binom{2}{4}$. – Dominik Sep 19 '15 at 16:08
• I would disagree about the binomial coefficient. The default meaning of "$2$ over $5$" or "$5$ over $2$" is not a binomial coefficient. – André Nicolas Sep 19 '15 at 16:22
• @AndréNicolas You're probably right, I couldn't find any source that supports my claim. I'm probably just used to the german pronunciation of binomial coefficients, which indeed uses the word "über", i.e. "over". – Dominik Sep 19 '15 at 16:27
• $\dbinom24$ is usually read as ‘2 choose 4’ (incidentally, it is equal to $0$). – Bernard Sep 19 '15 at 16:28