1 / 16

Monomials

Learn about monomials, constants, exponents, product of powers, and more in algebra, including rules and simplification techniques with detailed examples.

lcanter
Download Presentation

Monomials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Monomials Lesson 5-1 Algebra 2

  2. Vocabulary • Monomials - a number, a variable, or a product of a number and one or more variables • 4x, 20x2yw3, -3, a2b3, and 3yz are all monomials. • Constant – a monomial that is a number without a variable. • Base – In an expression of the form xn, the base is x. • Exponent – In an expression of the form xn, the exponent is n.

  3. Writing - Using Exponents Rewrite the following expressions using exponents: The variables, x and y, represent the bases. The number of times each base is multiplied by itself will be the value of the exponent.

  4. Writing Expressions without Exponents Write out each expression without exponents (as multiplication): or

  5. Product of Powers Simplify the following expression: (5a2)(a5) There are two monomials. Underline them. What operation is between the two monomials? Multiplication! • Step 1: Write out the expressions in expanded form. • Step 2: Rewrite using exponents.

  6. Product of Powers Rule For any number a, and all integers m and n, am • an = am+n.

  7. Multiplying Monomials If the monomials have coefficients, multiply those, but still add the powers.

  8. Multiplying Monomials These monomials have a mixture of different variables. Only add powers of like variables.

  9. Power of Powers Simplify the following: ( x3 )4 The monomial is the term inside the parentheses. • Step 1: Write out the expression in expanded form. • Step 2: Simplify, writing as a power. Note: 3 x 4 = 12.

  10. For any number, a, and all integers m and n, Power of Powers Rule

  11. Monomials to Powers If the monomial inside the parentheses has a coefficient, raise the coefficient to the power, but still multiply the variable powers.

  12. Monomials to Powers(Power of a Product) If the monomial inside the parentheses has more than one variable, raise each variable to the outside power using the power of a power rule. (ab)m = am•bm

  13. Monomials to Powers(Power of a Product) Simplify each expression:

  14. Division Powers Rule For any number a, and all integers m and n, am / an = am-n. • x114. 4xy -x5 24 x2y3 • 2. y105. xy3 • y20 y3z • 3. 6x3yz3 6. -4x5y2 • 12xy7z 26x3y7

  15. Negative Exponents • Never leave an answer with a negative exponent!! • The negative exponent simply means inverse. To eliminate the negative exponent, simply move only the variable and exponent with the negative exponent to the opposite of where it is located, numerator or denominator and drop the negative sign. 1. b-9b5 5. 3x-3y-9z-2 -12x-5y-1z-8 2. (3x2y5)(4x-5y7) 6. 3 -2 3. b-9b9 x-5 4. x -3 7. 3x3y 2 (2x3y4)-2

  16. Scientific Notation • For numbers in scientific notation there is one nonzero number before the decimal followed by the remaining numbers after the decimal and that number is multiplied by 10 to some power. • Find the scientific notation of the following: • 38, 200 • 0.00356 • 2,891 • (3 x 103)(2.1 x 10-6) • 8.8 x 109 • 2 x 10-3

More Related