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 Depdendent Variable

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 Dependent Variable

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# 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.

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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