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7.2

7.2. Properties of Rational Exponents. Learning Targets. Students should be able to… Use properties of rational expressions to evaluate and simplify expressions. Warm-up. Go over 7.1 Homework. Know the properties of exponents. Property: a m a n = a m+n Property: (a m ) n = a mn

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7.2

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  1. 7.2 Properties of Rational Exponents

  2. Learning Targets • Students should be able to… • Use properties of rational expressions to evaluate and simplify expressions.

  3. Warm-up

  4. Go over 7.1 Homework

  5. Know the properties of exponents • Property: aman = am+n • Property: (am)n = amn • Property: (ab)m = ambm • Property: • Property: a0 = 1 • Property: a-m • Property:

  6. Example 1: Simplify

  7. 2. Use properties to simplify expressions **Key – Look for similarities and then simplify** Since they are the same root we can multiply the insides Since they are the same root we can write under one radical

  8. 2. Use properties to simplify expressions **Key – Look for similarities and then simplify** Since they are not the same root we can’t multiply the insides. Instead, use Rational exponents Now add powers!

  9. 3. Write radicals in simplest form Rules to simplify • No negatives inside the radical (when even) • No fractions inside the radical • No radicals in the denominator • No perfect squares (or cubes, or 4th roots etc.) in the radical

  10. Lists of perfect squares, cubes, 4th powers, & 5th powers

  11. Example 4: Write in simplest form. Rewrite As a prime factorization Rewrite As a prime factorization Take out a 2 Multiply by to rationalize Simplify! Simplify!

  12. 4. Be able to add and subtract roots and radicals Example 5: Perform the indicated operation. Rewrite so you have like terms

  13. Be able to apply these rules to variable expressions.. Simplify the expression Add exponents in parentheses Rewrite with positive exponents Multiply exponents What is the relationship between the exponents? Subtract the x’s Add the z’s Reduce exponent

  14. Simplify the expression. What is the relationship between the exponents if they don’t divide evenly? Dividend goes outside, remainder stays inside.

  15. Closure

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