Powers and subscripts

Half the symbols in maths sit above or below the line: $x^2$, $a_1$, $e^{i\pi}$. Two characters do all of it, and one rule about braces keeps them in order.

Powers with ^

A caret raises the next character: x^2 gives $x^2$, and e^x gives $e^x$.

Subscripts with _

An underscore lowers the next character: a_1 gives $a_1$, x_n gives $x_n$. A subscript is how you number terms, label coordinates and name constants.

Braces: the one rule

^ and _ take only the next character. So x^10 gives $x^10$: the 1 is raised and the 0 is not. Put everything that belongs up or down in braces: x^{10} gives $x^{10}$.

Add braces to fix the formula below:

The same goes for subscripts: a_{n+1} gives $a_{n+1}$, and e^{2x} gives $e^{2x}$. When you are not sure, use braces anyway: x^{2} is exactly the same as x^2.

Both at once

A character can have a subscript and a power together. Type them in either order: x_1^2 and x^2_1 both give $x_1^2$, with the two stacked neatly.

Powers of powers

What is inside the braces can have its own power: e^{x^2} gives $e^{x^2}$, and 2^{2^n} gives $2^{2^n}$.

Typing x^2^3 is an error ("double superscript"), because LaTeX cannot tell which you mean. Say it with brackets or with braces: (x^2)^3 gives $(x^2)^3$, and x^{2^3} gives $x^{2^3}$.

Primes

An apostrophe gives a prime, for derivatives: f'(x) gives $f'(x)$, and f''(x) gives $f''(x)$. LaTeX raises it for you.

Words as subscripts

Letters in a subscript are italic, like any variable: T_{max} gives $T_{max}$, which reads as m times a times x. For a label that is a word, put the word in \text{...}: T_{\text{max}} gives $T_{\text{max}}$. There is more on \text in lesson 11.

Practise

In short

• ^ raises and _ lowers the next character.
• Anything longer than one character goes in braces: x^{10}, a_{n+1}.
• A subscript and a power can go in either order, and a power can hold another power in its braces.
• An apostrophe is a prime, and a word as a subscript goes in \text{...}.

Next, in lesson 3: fractions and roots.