Download Multiplication of Monomials

Multiplication of Monomials
Chapter 7.2
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Recall when a number is raised to a power the
number is the base and the exponent is the power.
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23: 2 is the base and 3 is the exponent.
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Variables can be raised to powers also.
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x5 : x is the base and 5 is the exponent.
Rule for Multiplying exponential Expressions
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If m and n are integers then,
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(xm)(xn)= x(m+n)
Examples with one Variable
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(x2)( x3)= x(2+3) = x5
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(x4 )( x5)= x(4+5) = x9
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(x)( x7)= x(1+7) = x8
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If a variable does not have an exponent it is
assumed to be raised to the power of 1.
Examples With Numerous Variables
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(3x2 )(6x3)
= (3)(6)(x2 x3)=18 x(2+3)
= 18x5
(-3xy2)(-4x2y3)
=(-3)(-4)(xx2)(y2y3))
=12x3 y5
(-x2y3)(11x9)
=(-1)(11)(x2 x9)(y3)
= -11x11y3
Simplify Monomials Raised to Powers.
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Rule for simplifying Powers of Exponential Expressions.
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(xm)n = xmn ; Just multiply the exponents.
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Rule for simplifying Powers of Products.
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(xmyn)p = xmp ynp Just multiply the exponents.
Examples of Exponential Powers
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1. (x2)5 =
x2*5 = x10
2. (x2y5)5 =
x2*5y5*5 = x10 y25
3. (3x2y5)3 =
(3)3 (x2)3( y5)3 = 27 x6y15
Examples: Recall PEMDAS
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1. (-2x) (-3xy2)3 =
(-2x)(-3)3 (x)3 (y2)3 = (-2)(-27) (xx3) (y6) =
54x4 y6
2. (3x) (2x2y2)3 =(3x) (2)3(x2)3(y2)3 =
(3*8)(xx6)(y6) =
24x7 y6
YOU TRY!
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1. (x9)5
2. (x2)15
3. (x2y8)5
4. (4x2y3)3
5. (3xy2)(-2x2y5)5
6. (-x2) (2x2 y2)5
Answers
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1. x45
2. x30
3. x10 y40
4. 64x6y9
5. -96x11y27
6. -32x12y10