Presentation on theme: "Multiplying Monomials and Raising Monomials to Powers"— Presentation transcript:
1Multiplying Monomials and Raising Monomials to Powers
2VocabularyMonomials - a number, a variable, or a product of a number and one or more variables4x, 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.
3Writing - 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.
4Writing Expressions without Exponents Write out each expression without exponents (as multiplication):or
5Product 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.
6Product of Powers Rule am • an = am+n. For any number a, and all integers m and n,am • an = am+n.
7Multiplying Monomials If the monomials have coefficients, multiply those, but still add the powers.
8Multiplying Monomials These monomials have a mixture of different variables. Only add powers of like variables.
9The monomial is the term inside the parentheses. Power of PowersSimplify the following: ( x3 ) 4The 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.
10Power of Powers RuleFor any number, a, and all integers m and n,
11Monomials to PowersIf the monomial inside the parentheses has a coefficient, raise the coefficient to the power, but still multiply the variable powers.
12Monomials 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
13Monomials to Powers (Power of a Product) Simplify each expression:
15Let's look at the rules.For all integers “m” and “n” and any nonzero number “a” ……When the problems look like this, and the bases are the same, you will subtract the exponents.ANY number raised to the zero power is equal to ONE.If the exponent is negative, it is written on the wrong side of the fraction bar, move it to the other side.
161.Subtract the exponents2.When dividing the coefficients or subtracting the exponents, place the answer on the side of the fraction bar that has the larger value for that term.Divide the coefficients
17If you’re having trouble with the rules, try it like this……… First, factor numerator and denominator into prime factors.Second, cross out like terms from top to bottom. (reduce)Third, list remaining terms and multiply them back together.
18U’s cancelEach other3.Subtract the exponents4.When dividing the coefficients or subtracting the exponents, place the answer on the side of the fraction bar that has the larger value for that term.Divide the coefficients
195.Remember, if the exponent is negative, the term is written on the wrong side of the fraction bar, move it to the other side.6.NowSubtractTheExponents
20Now divide the coefficients but now ADD the exponents Fix yournegativeexponent7.8.ANY number raised to the zero power is equal to ONE.
21Now divide the coefficients and combine the exponents Fix yournegativeexponents9.