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POWER EXPRESSIONS INVOLVING VARIABLES

POWER EXPRESSIONS INVOLVING VARIABLES. LESSON 18. EXPONENT LAWS. EXPONENT LAWS. EXPONENT LAWS. EXPONENT LAWS. EXPONENT LAWS. m n. m a n a. a. (. ). =. EXPONENT LAWS. m n. m a n a. a. (. ). =. EXPONENT LAWS. m n. m a n a. a. (. ). =. 1 x n. EXAMPLES.

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POWER EXPRESSIONS INVOLVING VARIABLES

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  1. POWER EXPRESSIONS INVOLVING VARIABLES LESSON 18

  2. EXPONENT LAWS

  3. EXPONENT LAWS

  4. EXPONENT LAWS

  5. EXPONENT LAWS

  6. EXPONENT LAWS m n ma na a ( ) =

  7. EXPONENT LAWS m n ma na a ( ) =

  8. EXPONENT LAWS m n ma na a ( ) = 1 xn

  9. EXAMPLES (4x3y2)(5x2y4) Solution (4x3y2)(5x2y4) means 4 * x3 * y2 * 5 * x2 * y4 We can multiply in any order. (4x3y2)(5x2y4) = 4 * 5 * x3 * x2 * y2 * y4 = 20x5y6

  10. 6 3 6 3 a5 a2 a5 a2 b3 b2 b3 b2 x x x x EXAMPLES 6a5b3 3a2b2 Solution 6a5b3 3a2b2 means 6a5b3 3a2b2 = = 2a3b

  11. x2 z3 x2 z3 x2 z3 ( ( ( )2 )2 )2 x2 z3 x2 z3 * x2 z3 x2 z3 * EXAMPLES Solution means = x4 z6 =

  12. EXAMPLES c-3 * c5 Solution c-3 * c5 = c-3+5 Same methods apply if some of the exponents are negative integers = c2

  13. EXAMPLES Same methods apply if some of the exponents are negative integers m2 * m-3 Solution m2 * m-3 = m2 +(-3) = m-1

  14. EXAMPLES Same methods apply if some of the exponents are negative integers (a-2)-3 Solution (a-2)-3 = a(-2)(-3) = a6 Remember exponent law #2 ( power of powers)

  15. EXAMPLES Same methods apply if some of the exponents are negative integers (3a3b-2)(15a2b5) Solution (3a3b-2)(15a2b5) means 3* 15 * a3 * a2 * b-2 * b5 We can multiply in any order. (3a3b-2)(15a2b5) = 3* 15 * a3 * a2 * b-2 * b5 = 45a5b3

  16. 42 7 42 7 X-1 x3 X-1 x3 y4 y-2 y4 y-2 x x x x EXAMPLES Same methods apply if some of the exponents are negative integers 42x-1y4 7x3y-2 Solution 42x-1y4 7x3y-2 means 42x-1y4 7x3y-2 = = 6x-4y6 6y6 x4 = Positive Exponents

  17. EXAMPLES Same methods apply if some of the exponents are negative integers (a-3b2)3 Solution (a-3b2)3 means a(-3)(3) * b(2)(3) (a-3b2)3 = a(-3)(3) * b(2)(3) = a-9b6 b6 a9 = Positive Exponents

  18. CLASSWORK • PAGE 294 • #3-8 • #9 (e,f,g,h,I,j) • #10 – 13 • Page 295 • #18, #20

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