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Multiplication Property of Radicals
Determining if a Function has an Inverse
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Degree of a Polynomial
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Factoring Trinomials by Grouping
The Slope of a Line
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Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
Solving Quadratic Equations
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Quotient Rule for Radicals
Prime Polynomials
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Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
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Expansion of a Product of Binomials
Solving Equations
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Solving Quadratic Equations by Factoring
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Rationalizing the Denominator
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The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
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Dividing Monomials
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Adding and Subtracting Functions
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Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Roots
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The Rectangular Coordinate System
Polar Form of a Complex Number
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Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
 

Quotient Rule for Radicals

The power of a quotient rule is also valid for integral and rational exponents. This rule allows us to write

These equations can be written using radical notation as

The power of a quotient rule (for the power 1/n) can be stated using radical notation. When written with radicals, it is called the quotient rule for radicals.

 

Quotient Rule for Radicals

The nth root of a quotient is equal to the quotient of the nth roots. In symbols,

provided that all of the expressions represent real numbers and b 0.

 

Helpful hint

We could get by without the rules for radicals. If we converted every radical expression to an exponential expression, then we could apply the rules for exponents. However, it is simpler to learn a few rules for radicals.

 

The quotient rule is used to simplify radicals by rewriting the root of a quotient as the quotient of the roots.

 

Example 2

Using the quotient rule to simplify radicals

Simplify each expression.

Solution

 
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