MULTIPLYING AND DIVIDING MONOMIALS

Example 1 :

Multiply. 

(4x²)(5x³)

Solution :

=  (4x²)(5x³)

Group factors with like bases together. 

=  (4 ⋅ 5)(x² ⋅ x³)

Use the Product of Powers Property. 

=  20x^{2 + 3}

=  20x⁵

Example 2 :

Multiply.

(-6a)(7b)

Solution :

=  (-6a)(7b)

  =  -(6 ⋅ 7)ab

  =  -42ab

Example 3 :

Multiply

(3p⁵/7)(14p²/9)

Solution :

=  (3p⁵/7)(14p²/9)

Group factors with like bases together. 

=  (3/7 ⋅ 14/9)(p⁵ ⋅ p²)

Use the Product of Powers Property. 

=  (2/3)(p^{5 + 2})

=  (2/3)p⁷ 

Example 4 :

Multiply. 

(pqr)(p²qr)

Solution :

=  (pqr)(p²qr)

Group factors with like bases together. 

=  (p ⋅ p²)(q ⋅ q)(r ⋅ r)

Use the Product of Powers Property. 

=  (p^{1 + 2})(q^{1 + 1})(r^{1 + 1})

=  (p³)(q²)(r²)

=  p³q²r²

Example 5 :

Simplify. Express your answer using positive exponents. 

(8x)(8x) / 4x⁴

Solution :

=  (8x)(8x) / 4x⁴

Group factors with like bases together. 

=  (8 ⋅ 8)(x ⋅ x) / 4x⁴

Use the Product of Powers Property. 

=  64x^{1 + 1} / 4x⁴

=  64x² / 4x⁴

=  16x² / x⁴

Use the Quotient of Powers Property.

=  16x^{2 - 4}

=  16x^-2

=  16/x²

Example 6 :

Simplify. Express your answer using positive exponents. 

(x³y⁵) / (xy²)

Solution :

(x³y⁵) / (xy²)

Group factors with like bases together. 

=  (x³/x) ⋅ (y⁵/y²)

Use the Quotient of Powers Property.

=  x^{3 - 1} ⋅ y^{5 - 2}

=  x²y³

Example 7 :

Simplify. Express your answer using positive exponents. 

(abc) / (a²bc)

Solution :

=  (abc) / (a²bc)

Group factors with like bases together. 

=  (a/a²) ⋅ (b/b) ⋅ (c/c)

Use the Quotient of Powers Property.

=  a^{1 - 2} ⋅ b^{1 - 1} ⋅ c^{1 - 1}

=  a^-1 ⋅ b⁰ ⋅ c⁰

=  1/a ⋅ 1 ⋅ 1

=  1/a

Example 8 :

Simplify. Express your answer using positive exponents. 

=  (-12x³y²) / (4xy⁵)

Solution :

=  (-12x³y²) / (4xy⁵)

Group factors with like bases together. 

=  (-12/4) ⋅ (x³/x) ⋅ (y²/y⁵)

Use the Quotient of Powers Property.

=  -3 ⋅ x^{3 - 1} ⋅ y^{2 - 5}

=  -3 ⋅ x² ⋅ y^-3

=  -3x²/y³

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