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P.2 INTEGER AND RATIONAL NUMBER EXPONENTS

P.2 INTEGER AND RATIONAL NUMBER EXPONENTS. ( الاسس الصحيحة والنسبية ). Objectives:. Properties of Exponents Scientific Notation Rational Exponents and Radicals Simplifying Radical Expressions. Def: If a is a real number and n is a positive integer, then. Ex:. Ex:. Ex:.

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P.2 INTEGER AND RATIONAL NUMBER EXPONENTS

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  1. P.2 INTEGER AND RATIONAL NUMBER EXPONENTS (الاسس الصحيحة والنسبية) Objectives: • Properties of Exponents • Scientific Notation • Rational Exponents and Radicals • Simplifying Radical Expressions

  2. Def: If a is a real number and n is a positive integer, then Ex: Ex:

  3. Ex:

  4. Laws of Exponents Law Example

  5. Ex: Simplify the following expression

  6. More Examples

  7. Converting a Decimal to Scientific Notation 1. Count the number N of places that the decimal point must be moved in order to arrive at a number x, where 1 <x< 10. 2. If the original number is greater than or equal to 1, the scientific notation is 3. If the original number is between 0 and 1, the scientific notation is

  8. Decimal notation 9 digits Decimal notation 4 digits Ex: Write the number 5,100,000,000 in scientific notation. 5,100,000,000.0 Ex: Write the number 0.00032 in scientific notation. 0 . 0 0 0 3 2

  9. Ex 0.000043

  10. Rational Exponents If a is a real number and n> 2 is an integer, then , the nth radical of a n is called the index of the radical a is called the radicand

  11. If a is a real number and m and n are integers containing no common factors with n> 2, then

  12. Radical (الرتبة) Index n x Radicand(المج|ور) Radicals (الج\ور)

  13. Properties of Rational Exponents If m and n represent rational numbers and a and b are positive real number, then

  14. Ex: Simplify

  15. Square Roots

  16. (الج|ر الرئيسي) Square Roots continued

  17. Expressions in the form

  18. Simplifying

  19. Higher Order Roots Having an Index Larger than 2

  20. Ex:

  21. Ex:

  22. Ex: Simplify:

  23. Multiplying Radicals

  24. Ex:

  25. Dividing Radicals

  26. Simplifying A Radical: For a radical to be simplified, the radicand cannot contain any factors that are perfect roots (i.e. exponents are evenly divisible by the index). To simplify the radical we do the following : • Factor the radicand into prime factors using exponential notation (or, express the radicand as a product of factors in which one factor is the largest perfect nth power possible).

  27. Use the product rule and the laws of exponents to rewrite the radical as a product of two radicals such that: • First radicand: contains factors that are perfect roots (i.e. exponents are evenly divisible by the index). • Second radicand: contains factors are not perfect roots (the indices are smaller than the index). Extract the perfect root from the first radicand.

  28. Like Radicals: Addition/Subtraction Ex: Simplify

  29. Ex:

  30. Ex: Simplify

  31. Rationalizing Denominators (انطاق الج|ور) • For an expression containing a radical to be in simplest form, a radical cannot appear in the denominator • The process of removing a radical from the denominator or the numerator of a fraction is calledrationalizing the denominator.

  32. Ex: Rationalize the denominator of the following expressions: Multiply by the conjugate Simplify

  33. Ex: Simplify each expression. Express the answer so only positive exponents occur.

  34. You’re shining!

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