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Multiplying Monomials

Monomials

A monomial is a number, a variable, or a product of a number and one or more variables.

The only rules are that the variables should be raised to only positive integer powers (no square roots or 1 x 's allowed), and no plus or minus signs.

Examples:

17 , 3xy , 4 x 2 ,

7 100 a 5 b 6 c 7 d 8 z 999

 

Multiplication of Monomials

When you multiply monomials, first multiply the coefficients and then multiply the variables by adding the exponents.

Examples:

1) 4 2 4 3 = 4 2+3 = 4 5 2) x 2 x 5 = x 2+5 = x 7 3) 4 2 x 5 =16 x 5 =16 x 5 4)( 2 a 2 b )( 5 a 3 b 2 )=( 25 )( a 2+3 )( b 1+2 ) =10 a 5 b 3 5)( 2 a 2 b )( 5 a 3 b 2 )( abc )=( 25 )( a 2+3+1 )( b 1+2+1 )( c ) =10 a 6 b 4 c

Note that when you multiply monomials with same base, you can add their exponents.

a m a n = a m+n

This is called the Product of Powers Property.