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AF 2.1 & 2.2 Rules of Exponents/Monomials

AF 2.1 & 2.2 Rules of Exponents/Monomials. Monomial. Monomial - is a term such as 4x. Includes a number and one or more variables. Example: 5x, 3x 2. Like Terms .

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AF 2.1 & 2.2 Rules of Exponents/Monomials

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  1. AF 2.1 & 2.2Rules of Exponents/Monomials

  2. Monomial • Monomial- is a term such as 4x. Includes a number and one or more variables. Example: 5x, 3x2

  3. Like Terms • Like terms are made up of exactly the same variable and the same powers of these variables. In the phrase 2x+3x, the items 2x and 3x are called like terms. Example: Simplify by adding similar or like terms. 2x+4+3x-1 <---- *2x and 3x are like terms. *4 and -1 are like terms. On your paper, combine the like terms and simply the expression.

  4. Answer: 2x+4+3x-1 =5x+3

  5. Whiteboard CFU! Which of the following is a monomial? • 12x • x-y • 4x2

  6. Multiplying Monomials Using the Commutative Property • Commutative Property: We can multiply in any order and the product is the same: a x b = b x a a2b2 = b2a2

  7. Remember! When you are multiplying with identical bases, you simply add the exponents in order to simplify.

  8. Example: a2 X a3 (a x a) X ( a x a x a) -------- = a5 --------

  9. Whiteboard CFU! Commutative property says…. n2 X m is the same as _______ x2 X z2 is the same as _______ p3 X s2 is the same as _______

  10. Whiteboard CFU! 23 X 22 • Write in expanded form__________ • Simplify the following: __________

  11. Whiteboard CFU! • Simplify the following: 5b + 2c +3b + 2 - 5= __________

  12. Whiteboard CFU! • Simplify the following: -4a + (-5a) + 3 - 7 = __________

  13. AF 2.2- Powers of Monomials • An exponent tells how many times a number or variable is used as factor: BIG NOTE: Power of a Power. For any number x, and all integers a and b: (xa )b = xab Example: (23)2= 2 x 2 x 2 x 2 x 2 x 2 = 26

  14. Dividing Monomials • x5/x2 = xxxxx ÷ xx= x3 BIG Note: Cancel x/x as 1 Example: Simplify m5 n3/ m2n= ____________ <---Expanded form =_______________ <--- Simplest form

  15. Whiteboard CFU! x4y4z4 / x4y2z a3b2c5 / a2bc4

  16. Squares and Square Roots of Monomials • To find the square root of a monomial with a variable, • Break into numbers and letters • Find the square root of each part Example: √9x4 = √9 √x4 <------- Think: What expression do you multiply by itself to get x4 = 3 x2 =3x2

  17. Whiteboard CFU! Find the square roots of the following: • 25= • 121= • n6= • z4=

  18. Whiteboard CFU! e) √16y2 f) √36n10

  19. Independent Practice AF 2.1 Simplify each expression: • 4x+2+x-1 • 2a+5+a+2 • 5a-2b+4+2a+b+2 • 4x+5y+6+3x+y • r+1+2r+2r-3 • 3x-(2x+4)+2 • 34 x36 • x2 x2x3

  20. Write each of the following in expanded form and evaluate: 1. (5x)3 2. 3. (11z)3 4. (4x)2 5. (2x2y)2 6. x2 y5/ x3 y2 7. a4 b2/ a3 b2 8. 18a4 n5/ 3a3 n 9. xyz/xyz Find the square roots: 10. √100x8 11. √49g2 12. √4g2h2 13. √25x2y6 14. √64m4 15. √16x2y2z2 16. √4r10 17. √9y10 18. √81z2 Independent Practice AF 2.2

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