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 Dependent Variable

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# Multiplying Monomials

## Multiplying a Monomial by a Monomial

To find the product of two monomials, multiply the coefficients. Then, use the Multiplication Property of Exponents to combine variable factors that have the same base.

Example 1

Find: 7m3n4 Â· 6mn2

Solution

 Write the coefficients next to each other. Write the factors with base m next to each other, and write the factors with base n next to each other. 7m3n4 Â· 6mn2 = (7 Â· 6)(m3 Â· m1)(n4 Â· n2) Use the Multiplication Property of Exponents. = (7 Â· 6)(m3 + 1)(n4 + 2) Simplify. = 42m4n6

Remember:

Multiplication Property of Exponents: xm Â· xn = xm + n

Example 2

Find:

Solution

 Write the coefficients next to each other. Write the factors with base w next to each other, and write the factors with base y next to each other. Use the Multiplication Property of Exponents. Simplify. = 2w5x7y6

Example 3

Find: (-5x3y)(3x5)(2xy5)

Solution

 Write the coefficients next to each other. (-5x3y)(3x5)(2xy5) Write the factors with base x next to each other and write the factors with base y next to each other. = (-5 Â· 3 Â· 2)(x3 Â· x5 Â· x1)(y1 Â· y5) Use the Multiplication Property of Exponents. Simplify. = (-5 Â· 3 Â· 2)(x3 + 5 + 1)(y1 + 5) = -30x9y6