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, 20x 2 yw 3, -3, a 2 b 3, and 3yz are all monomials. Constant – a monomial that is a number without a variable. Base – In an expression of the form x n, the base is x. Exponent – In an expression of the form x n, 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. Simplify the following expression: (5a 2 )(a 5 )  Step 1: Write out the expressions in expanded form.  Step 2: Rewrite using exponents. Product of Powers There are two monomials. Underline them. What operation is between the two monomials? Multiplication!

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

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

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

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

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

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 = a m b m

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

14. For any number a, and all integers m and n, a m / a n = a m-n. Division Powers Rule 1.x 11 4. 4xy -x 5 24 x 2 y 3 2. y 10 5. xy 3 y 20 y 3 z 3. 6x 3 yz 3 6. -4x 5 y 2 12xy 7 z 26x 3 y 7

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  b 5 5. 3x -3 y -9 z -2 -12x -5 y -1 z -8 2. (3x 2 y 5 )(4x -5 y 7 ) 6. 3 -2 3. b -9  b 9 x -5 4. x -3 7. 3x 3 y 2 (2x 3 y 4 ) -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: 1.38, 200 2.0.00356 3.2,891 4.(3 x 10 3 )(2.1 x 10 -6 ) 5.8.8 x 10 9 2 x 10 -3