Download Algebra 8-1 Multiplying Monomials

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)
4
2
=(a•a)(b •b )
2
6
=a b
Example 5
(-7c3d4)(4cd3)
3
4
3
= -7•4•c •c•d •d
4
7
= -28c d
Example 6
2
2
3
(4cd) (-3d )
=(16c2d2)(-27d6)
=16• -27•c2•d2•d6
= -432c2d8