Math - Exponent

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

Example:

5 to the power of 3 is interpreted as:

• $5^3$
• $5 * 5 * 5$
• $125$

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.
Any number without an explicit exponent has an exponent of 1.

$x^1 = x\\ 5^1 = 5$

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:
  $x^{\frac{m}{n}} = \sqrt[n]{x^m}$