Exponents and Subscripts

Exponents

• To use exponents, we use the ^ symbol to display the succeeding character as the exponent of the preceding character.

  • For example:
    • a^b displays as .
    • (a+b)^2 \ne a^2 + b^2 displays as .

• However, this breaks down when we attempt to exponentiate two or more characters:

  • x^a x^b= x^(a+b) displays as

• Instead, we use grouping symbols {}.

  • These symbols are reserved to group multiple characters at once, often when we apply an effect to two or more characters.
  • In this case, we group the characters we want to exponentiate, x^a x^b = x^{(a + b)}.
  • This would then treat the entire group as an exponent of :

• Some more examples include:

  • e^{x^2} displays .
  • 2^{10000} displays .
  • e^{x\ln(2x+1)} displays .

Subscripts

• To apply subscripts, we now use the _ symbol to display the succeeding character in subscript.

  • For example:
    • x_1 displays
    • \log_{2}(x) displays

• Similar to exponents, we use grouping symbols {} to group two or more characters that we want to put in subscript form.

  • For example:
    • f_{10}(x) displays
    • 1336_{16} displays