8-1 Multiplying Monomials This presentation was created following the Fair Use Guidelines for...

8-1 Multiplying Monomials

This presentation was created following the Fair Use Guidelines for Educational Multimedia. Certain materials are included under the Fair Use exemption of the U. S. Copyright Law. Further use of these materials and this presentation is

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Objectives

• Students will multiply monomials.

• Students will simplify expressions involving powers of monomials.

Vocabulary

• Monomial – a number, variable, or a product of numbers and variables. An expression involving a variable in the denominator is NOT a monomial.

• Constant – a monomial that is a real number

• Examples of monomials: -5, x, ½a2

Properties

• Product of Powers – to multiply two powers that have the same base, add the exponents

• Example 1:(5x4)(6x7)

(5•6)(x4•x7)

30x11

Properties

• Power of a Power – to find a power of a power, multiply the exponents.

• Example 2:

(k4)5

k20

Because (k4)5 means (k4)(k4)(k4)(k4)(k4) and if we add the exponents, we get k20.

Properties

• Power of a Product – to find the power of a product, find the power of EACH factor and multiply.

• Example 3: (-2xy)3

=(-2)3(x3)(y3)

= -8x3y3

Simplifying Monomial Expressions

To simplify an expression involving monomials, write an equivalent expression in which:

• Each base appears exactly once

• There are no powers of powers

• All fractions are in simplest form.

Example 4

(ab4)(ab2)

=(a•a)(b4•b2)

=a2b6

Example 5

(-7c3d4)(4cd3)

= -7•4•c3•c•d4•d3

= -28c4d7

Example 6

(4cd)2(-3d2)3

=(16c2d2)(-27d6)

=16• -27•c2•d2•d6

= -432c2d8