 # Rational Exponents When a base is raised to a rational exponent of the form 1/n we use the following definition: The denominator of the rational exponent.

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Rational Exponents When a base is raised to a rational exponent of the form 1/n we use the following definition: The denominator of the rational exponent … … becomes the index of the radical... …and the base of the exponential … … becomes the radicand of the radical.

Example 1 Write each of the following using radical notation. Simplify the radical if possible:

Example 2 Write each of the following in rational exponent form:

When a base is raised to a rational exponent of the form m/n we use the following definition: The numerator m becomes the …exponent.

When a base is raised to a rational exponent of the form m/n we use the following definition: The numerator m becomes the …exponent. The denominator n becomes the …index.

When a base is raised to a rational exponent of the form m/n we use the following definition: The numerator m becomes the …exponent. The denominator n becomes the …index. The base b becomes the …radicand.

Example 3 Write the following using radical notation. Simplify the radical if possible: or

Whenever the radical can be simplified easily, the second form is the one to use. Example 4

Example 5 Write the following in rational exponent form:

When a base is raised to a negative rational exponent we use the following definition:

When a rational base is raised to a negative rational exponent we use the following: Take the reciprocal of the rational expression and make the exponent positive.

Example 6 Write the following using positive exponents. Simplify if possible:

Example 7

Example 8 Take the reciprocal of the rational expression and make the exponent positive.

Example 8

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