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Master Operations with Rational Exponents

Learn to perform operations with rational exponents, convert between radical and rational form, and simplify expressions. Practice changing bases and simplifying radicals to enhance your understanding.

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Master Operations with Rational Exponents

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  1. 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)

  2. 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]

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

  4. Determine if each expression is equivalent or not. Hint: Change Expressions all to rational exponents 1. and 2. and 3. 4. and and 6. 5. and and

  5. 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.

  6. PRACTICE: Simplify each expression into simplest radical form 2. 1. 3. 4. 5. 6.

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

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

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