8-1 Multiplying Monomials

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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