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SPECIAL FRACTION EXPONENT :

Learn about special fraction exponents, also known as radicals, their properties, operations, and simplification techniques. Transform rational exponents to radical form and vice versa with step-by-step examples. Enhance your mathematical skills today!

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SPECIAL FRACTION EXPONENT :

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  1. 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?

  2. Special Fraction Exponents, , are more commonly known as radicals in which the N value represents the root or index of the radical. Index 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 Prime Factorization: Factor the Radicand Completely Write the base of all perfect squares (PAIRS) outside of the radical as product Everything else (SINGLES) stays under the radical as a product.

  3. 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) 2) 3) 4) 5) 6)

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

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

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

  7. 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.

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

  9. 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. 3. 3. 4.

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

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