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Bell Ringer 3/27

This lesson focuses on reviewing the laws of exponents and distinguishing between rational and irrational numbers. It covers topics such as exponential form, multiplying and dividing powers, power of a power, product and quotient law of exponents, negative law of exponents, and zero law of exponents. Students will also learn how to classify numbers as rational, irrational, or not a real number.

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Bell Ringer 3/27

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  1. Bell Ringer 3/27 • Solve for x: 2x + 7 = -23 X = -15 3x – 4 = 11 X = 5

  2. Objective • Review Exponent Rules and Rational Numbers • Guided practice • Daily Class Assessment

  3. The Laws of Exponents MGSE 8.EE.3

  4. Exponents exponent Power base 53 means 3 factors of 5 or 5 x 5 x 5

  5. The Laws of Exponents: #1: Exponential form:The exponent of a power indicates how many times the base multiplies itself. n factors of x

  6. #2: Multiplying Powers:If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS! So, I get it! When you multiply Powers, you add the exponents!

  7. #3: Dividing Powers:When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS! So, I get it! When you divide Powers, you subtract the exponents!

  8. #4: Power of a Power:If you are raising a Power to an exponent, you multiply the exponents! So, when I take a Power to a power, I multiply the exponents

  9. #5: Product Law of Exponents:If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent. So, when I take a Power of a Product, I apply the exponent to all factors of the product.

  10. #6: Quotient Law of Exponents:If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient.

  11. #7: Negative Law of Exponents:If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha! If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!

  12. #8: Zero Law of Exponents:Any base powered by zero exponent equals one. So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.

  13. SOLUTIONS

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  18. SOLUTIONS

  19. Rational and Irrational Numbers Essential Question How do I distinguish between rational and irrational numbers?

  20. Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Reals Rationals -2.65 Integers -3 -19 Wholes 0 Irrationals Naturals 1, 2, 3...

  21. Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals. 4 5 23 3 = 3.8 = 0.6 1.44 = 1.2

  22. Irrational numberscan be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational. Caution! A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.

  23. A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.

  24. 9 = 3 81 3 9 3 = = 3 Check It Out! Example 1 Rational, Irriational, Not a Real Number 9 1. rational –35.9 –35.9 is a terminating decimal. 2. rational 81 3 3. rational

  25. 0 3 = 0 Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number. 4. 21 irrational 0 3 5. rational

  26. Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number. 4 0 6. not a real number

  27. Check It Out! Example 2 State if each number is rational, irrational, or not a real number. 7. 23 is a whole number that is not a perfect square. 23 irrational 9 0 8. not a real number

  28. 8 9 8 9 64 81 = Check It Out! Example 2 State if each number is rational, irrational, or not a real number. 64 81 9. rational

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