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Understanding Rational Exponents and Their Properties: A Comprehensive Guide

This assignment provides a detailed exploration of rational exponents, covering essential terminology such as base and variable expressions. It includes important examples that illustrate how to substitute and evaluate expressions with specific variables. The guide explains multiplication and division properties of exponents, including the product of powers and power of a quotient, along with the treatment of zero and negative exponents. Step-by-step solutions to problems enhance comprehension, making it a valuable resource for mastering the fundamental concepts of exponents.

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Understanding Rational Exponents and Their Properties: A Comprehensive Guide

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  1. RATIONAL EXPONENTS Assignments Assignments

  2. Basic Terminology EXPONENT means BASE Important Examples

  3. IMPORTANT EXAMPLES Variable Examples

  4. Variable Expressions

  5. Substitution and Evaluating STEPS Write out the original problem. Show the substitution with parentheses. Work out the problem. =64 More Examples

  6. Evaluate the variable expression when x = 1, y = 2, and w = -3 Step 1 Step 1 Step 1 Step 2 Step 2 Step 2 Step 3 Step 3 Step 3

  7. This property is used to combine 2 or more exponential expressions with the SAME base. MULTIPLICATION PROPERTIES PRODUCT OF POWERS

  8. This property is used to write and exponential expression as a single power of the base. MULTIPLICATION PROPERTIES POWER TO A POWER

  9. This property combines the first 2 multiplication properties to simplify exponential expressions. MULTIPLICATION PROPERTIES POWER OF PRODUCT

  10. PRODUCT OF POWERS MULTIPLICATION PROPERTIES ADD THE EXPONENTS POWER TO A POWER MULTIPLY THE EXPONENTS SUMMARY POWER OF PRODUCT

  11. ZERO AND NEGATIVE EXPONENTS ANYTHING TO THE ZERO POWER IS 1.

  12. This property is used when dividing two or more exponential expressions with the same base. DIVISION PROPERTIES QUOTIENT OF POWERS

  13. DIVISION PROPERTIES Hard Example POWER OF A QUOTIENT Summary of Zero, Negative, and Division Properties

  14. ZERO, NEGATIVE, AND DIVISION PROPERTIES Zero power Quotient of powers Negative Exponents Power of a quotient

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