SPECIAL FRACTION EXPONENT The exponent is most often

SPECIAL FRACTION EXPONENT: The exponent is most often used in the power of monomials. Examples: Do you notice any other type of mathematical symbols that these special fraction exponents represent?

Special Fraction Exponents, , are more commonly known as radicals in which the N value represents the root or index of Index the radical. Radical Symbol Radicals: Radicand Note: The square root or ½ exponent is the most common radical and does not need to have the index written. Steps for Simplifying Square Roots 1. Prime Factorization: Factor the Radicand Completely 2. Write the base of all perfect squares (PAIRS) outside of the radical as product 3. Everything else (SINGLES) stays under the radical as a product.

Operations with Rational (Fraction) Exponents The same operations of when to multiply, add, subtract exponents apply with rational (fraction) exponents as did with integer (whole) exponents • Hint: Remember how to find common denominators and reduce. 1) 4) 2) 5) 3) 6)

Radicals (Roots) and Rational Exponent Form Rational Exponents Property: OR OR Example 1: Change Rational to Radical Form A] Example 2: A] B] C] Change Radical to Rational Form B] C]

Radicals Classwork # 1 – 4: Write in rational form. 1. 2. 3. 4. 7. 8. #5 – 8: Write in radical form. 5. 6.

Radicals Classwork #2 Determine if each pair are equivalent statements or not. 1. 3. 5. and and 2. 4. 6. and and

Simplifying Rational Exponents • Apply normal operations with exponents. • Convert to radical form. • Simplify the radical expression based on the index and radicand. 1. 2. 3. 4. 5. 6. 7. 8.

Radicals Classwork #3 Simplify the following expressions into simplest radical form 1. 4. 2. 5. 3. 6.

Change of Base (Index or Root) • Write the radicand in prime factorization form • REDUCE the fractions of Rational Exponents to rewrite radicals. 1. 2. 3. 4. 3.

Change of Base Practice Problems 1. 4. 2. 5. 3. 6.