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)

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

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

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

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

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

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