Monomials Multiplying Monomials and Raising Monomials to Powers

Monomials Multiplying Monomials and Raising Monomials to Powers

Vocabulary • Monomials - a number, a variable, or a product of a number and one or more variables • 4 x, 20 x 2 yw 3, -3, a 2 b 3, and 3 yz 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.

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.

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

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

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

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

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

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

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

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

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

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

What about dividing monomials?

1. Be able to divide polynomials 2. Be able to simplify expressions involving powers of monomials by applying the division properties of powers.

Simplify: Step 1: Rewrite the expression in expanded form Step 2: Simplify. Remember: A number divided by itself is 1. For all real numbers a, and integers m and n:

Simplify: Step 1: Write the exponent in expanded form. For all real numbers a and b, and integer m: Step 2: Multiply and simplify.

Apply quotient of powers Apply power of a quotient Apply quotient of powers. Apply power of a quotient. Apply power of a power Simplify

THINK! x 3 -3 = x 0 = 1 1. 2.