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Pythagorean theorem

The relationship among the three sides of a right triangle if $a$ and $b$ are the lengths of the legs (the two sides that form a right angle) and $c$ is the length of the hypotenuse (the side across from the right angle). \({c^2} = {a^2} + {b^2}\) \(c = \sqrt {{a^2} + {b^2}} \)

 

Pure imaginary number

A complex number of the form $bi$ where \(b \ne 0\).
 

Proportion

A statement that equates two ratios.

 

Product rule for radicals

Let $a$ and $b$ be real numbers, variables, or algebraic expressions. If the $n$th roots of $a$ and $b$ are real, then the following property is true \(\sqrt[n]{{ab}} = \sqrt[n]{a}•\sqrt[n]{b}\).

 

Product and power rules of exponents

Let $m$ and $n$ be positive integers and let $a$ and $b$ be real numbers, variables, or algebraic expressions. Product Rule: \({a^m}•{a^n} = {a^{m + n}}\) . Power-to-power rule: \({\left( {{a^m}} \right)^n} = {a^{mn}}\). Product to power rule: \({\left( {ab} \right)^m} = {a^m}{b^m}\).

 

Product

The result of multiplication of one number by another.
 

Principal nth root of a number

Let $a$ be the real number that has at least one real number $n$th root. The $n$th root has the same sign as $a$ and is denoted by the radical \(\sqrt[n]{a}\).

 

Prime polynomials

A nonfactorable polynomial.

 

Prime number

An integer greater than 1 with no factors other than itself and 1.

 

Power

An expression, such as 23, that represents a product formed by a repeated factor.

 
Glossary: P

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