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VAL JOSEPH DE GUZMAN

This guide covers the essential laws of exponents, including the first, second, third, and fourth laws. Each law is explained with equations and examples to illustrate the concepts accurately. Learn how to simplify expressions with exponents, apply negative exponents, and understand fractional exponents. Activities are included to practice transforming and simplifying various exponent expressions. Master these fundamental laws of exponents to enhance your mathematical skills and confidence.

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VAL JOSEPH DE GUZMAN

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  1. EXPONENTS VAL JOSEPH DE GUZMAN

  2. Laws of Exponents

  3. First Law of exponent It is in the form “anam” where both n and m are exponents. Solution: an+m Example:23(22) =23+2 =25 =32

  4. Second Law of Exponents It is in the form “an/am”. Solution: a. If n is greater than m use an-m b. If n is less than m use 1/an-m Example:23/22 =23-2 =2

  5. Third Law of Exponents It is in the form “(an)m”. Solution:anm Example:(32)4 =32(4) =38 =6561

  6. Fourth Law of Exponents If you had encounter an equation like this “(anbm)r”. Solution:arnbrm Example:(43 x 32)2 =46 x 34 =4096 x 81 =331,776

  7. Activity Simplify each of the following. 1. b2 X b3 7. (xy3)(x2yz3)3 2. c4/c3 8.a4b2c3/abc 3. (42 x 32)2 9. a2b2/a2b2 4. (a3b2)(a2b) 10. 4a3b4/2ab 5. (x2y3)2 11. (a6b2)6 6. B2 x aB2 12. 2a2 x a4

  8. Negative Exponents

  9. Equations like “a-1” is the same as “1/a”. Example:1) 2-2 =1/22 =1/4 2) 3-4 =1/34 =1/81

  10. Activity Transform each equation into an equation with a positive exponent. 1. 5-4 5. (ab3)-1 2. (3-2)-3 6. xy-3 3. (1/5)-3 7. (a+b)-2(a-2+b-2) 4. 2-1+3-2

  11. Fractional Exponents

  12. An expression like “an/m” is the same as the the expression “ m√an Example:1)33/2 =√33 =√27 2)82/3 =3√82 =3√64 =4

  13. Activity Express each with positive exponents. • 91/2 • 9-1/2 • (a/b)-1/2 • (x2y3)1/4

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