Math - Exponent

The exponent of a number indicates how many times the number should multiply itself.

$x^n\\ 5^4 = 625\\ 5*5*5*5 = 625$

The default exponent is 1: $x = x^{1}$

Negative Exponent

The negative exponent means the reciprocal of $x$ raised to the power of $n$.

$x^{-n} = \frac{1}{x^n}\\ 8^{-3} = \frac{1}{8^3}$

Exponent 0 & 1

The exponent 1 means the number itself.

x^1 = x
5^1 = 5

The exponent 0 means the number 1.

x^0 = 1
5^0 = 1

Exponent Rules

• Product Rule:
  $x^m \times x^n = x^{m + n}$
• Quotinent Rule:
  $x^m / x^n = x^{m - n}$
• Power of Power Rule:
  $(x^m)^n = x^{m \times n}$
• Power of a Product Rule:
  $(xy)^n = x^n y^n$
• Power of a Quotinent Rule:
  $(\frac{x}{y})^n = \frac{x^n}{y^n}$
• Fractional Exponent Rule:
  $x^{\frac{m}{n}} = \sqrt[n]{x^m}$