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Rational Exponents Fraction Exponents

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**Radical expression and Exponents**

By definition of Radical Expression. The index of the Radical is 3.

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**How would we simplify this expression?**

What does the fraction exponent do to the number? The number can be written as a Radical expression, with an index of the denominator.

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**The Rule for Rational Exponents**

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Write in Radical form

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Write in Radical form

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**Write each Radical using Rational Exponents**

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**Write each Radical using Rational Exponents**

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**What about Negative exponents**

Negative exponents make inverses.

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**What if the numerator is not 1 Always remember:**

Evaluate

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**What if the numerator is not 1**

Evaluate

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**What if the numerator is not 1**

Evaluate

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**For any nonzero real number b, and integer m and n**

Make sure the Radical express is real, no b<0 when n is even.

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**Simplify each expression**

No fraction in the denominators.

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**Simplify each expression**

No fraction in the denominators.

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Simplify

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Simplify

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Simplify

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**Simplify in simplest radical form**

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Radical form: Do # 68

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**Simplifying exponential expressions**

If in radical form, transform to exponential form Simplify by applying the exponent to each base. Express with positive exponents or radical form, depending on the directions

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**Express in simplest form**

Make exponential first!

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**Express in simplest form**

Make exponential first! Now simplify

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**Express in simplest form**

Make exponential first! Now simplify

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Next example Use positive exponents only!

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Next example Use positive exponents only! Or in radical form:

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Simplify

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Simplify

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Simplify

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Simplify

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