Tidewater Community College Intermediate Algebra Rational Exponents Mr. Joyner Tidewater Community College

Radicals (also called roots) are directly related to exponents. Intermediate Algebra Rational Exponents Radicals (also called roots) are directly related to exponents.

Intermediate Algebra Rational Exponents All radicals (roots) can be written in a different format without a radical symbol.

This different format uses a rational (fractional) exponent. Intermediate Algebra Rational Exponents This different format uses a rational (fractional) exponent.

Intermediate Algebra Rational Exponents When the exponent of the radicand (expression under the radical symbol) is one, the rational exponent form of a radical looks like this: Remember that the index, n, is a whole number equal to or greater than 2.

Intermediate Algebra Rational Exponents Examples: base When a base has a fractional exponent, do not think of the exponent in the same way as when it is a whole number. When a base has a fractional exponent, the exponent is telling you that you have a radical written in a different form.

Intermediate Algebra Rational Exponents For any exponent of the radicand, the rational exponent form of a radical looks like this:

How do you simplify ? Intermediate Algebra Rational Exponents Reduce the rational exponent, if possible. You can rewrite the expression using a radical. Simplify the radical expression, if possible. Write your answer in simplest form.

Intermediate Algebra Rational Exponents Example:

Intermediate Algebra Rational Exponents Examples:

Intermediate Algebra Rational Exponents Examples: No real number solution

See the chart on page 389 of your text. Intermediate Algebra Rational Exponents The basic properties for integer exponents also hold for rational exponents as long as the expression represents a real number. See the chart on page 389 of your text.

Intermediate Algebra Rational Exponents Example: What would the answer above be if you were to write it in radical form?

Intermediate Algebra Rational Exponents Example:

See the next two slides for a quick review. Intermediate Algebra Rational Exponents Do you remember the basic Rules of Exponents that you learned in Roots and Radicals? See the next two slides for a quick review.

The Square Root Rules (Properties) Intermediate Algebra Rational Exponents The Square Root Rules (Properties) Multiplication Division b may not be equal to 0.

The Cube Root Rules (Properties) Intermediate Algebra Rational Exponents The Cube Root Rules (Properties) Multiplication Division b may not be equal to 0.

The more general rules for any radical are as follows … Intermediate Algebra Rational Exponents The more general rules for any radical are as follows …

The Rules (Properties) Intermediate Algebra Rational Exponents The Rules (Properties) Multiplication Division b may not be equal to 0.

These same rules in rational exponent form are as follows … Intermediate Algebra Rational Exponents These same rules in rational exponent form are as follows …

The Rules (Properties) Intermediate Algebra Rational Exponents The Rules (Properties) Multiplication Division b may not be equal to 0.

Intermediate Algebra Rational Exponents In working with radicals, whether in radical form or in fractional exponent form, simplify wherever and whenever possible. What is the process for simplifying radical expressions?

Intermediate Algebra Rational Exponents Simplifying radicals – A radical expression is in simplest form once ALL of the following conditions have been met.… the radicand (expression under the radical symbol) cannot be written in an exponent form with any factor having an exponent equal to or larger than the index of the radical; there is no fraction under the radical symbol; there is no radical in a denominator.

Intermediate Algebra Rational Exponents Examples – Simplifying Radical Expressions: