MULTIPLYING  MONOMIALS WORKSHEET

Problem 1 :

Multiply. 

(4x²)(5x³)

Problem 2 :

Multiply. 

(-7x)(3y)

Problem 3 :

Multiply. 

(3/7)x⁵ ⋅ (14/9)x²

Problem 4 :

Multiply. 

(x³y⁵)(xy²)

Problem 5 :

Multiply. 

(xyz)(x²yz)

Problem 6 :

Multiply. 

(a²b²c³)(abc²)

Problem 7 :

Multiply. 

(4ab)(3a²b²)(2a³b³)

Problem 8 :

Multiply. 

(0.5a³b)(a²c²)(6b²)

Problem 9 :

Multiply. 

(-3x³y²)(4xy⁵)

Problem 10 :

Multiply. 

(-2pq³)(5p²q²)(-3q⁴)

Detailed Answer Key

Problem 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

Problem 2 :

Multiply. 

(-7x)(3y)

Solution :

=  -7x ⋅ 3y

=  (-7 ⋅ 3)xy

=  -21xy

Problem 3 :

Multiply. 

(3/7)x⁵ ⋅ (14/9)x²

Solution :

=  (3/7) x⁵ ⋅ (14/9) x²

Group factors with like bases together. 

=  (3/7 ⋅ 14/9)(x⁵ ⋅ x²)

Use the Product of Powers Property. 

=  (2/3)(x^{5 + 2})

=  (2/3)x⁷ 

Problem 4 :

Multiply. 

(x³y⁵)(xy²)

Solution :

=  (x³y⁵)(xy²)

Group factors with like bases together. 

=  (x³ ⋅ x)(y⁵ ⋅ y²)

Use the Product of Powers Property. 

=  (x^{3 + 1})(y^{5 + 2})

=  (x⁴)(y⁷)

=  x⁴y⁷

Problem 5 :

Multiply. 

(xyz)(x²yz)

Solution :

=  (xyz)(x²yz)

Group factors with like bases together. 

=  (x ⋅ x²)(y ⋅ y)(z ⋅ z)

Use the Product of Powers Property. 

=  (x^{1 + 2})(y^{1 + 1})(z^{1 + 1})

=  (x³)(y²)(z²)

=  x³y²z²

Problem 6 :

Multiply. 

(a²b²c³)(abc²)

Solution :

=  (a²b²c³)(abc²)

Group factors with like bases together. 

=  (a² ⋅ a)(b² ⋅ b)(c³ ⋅ c²)

Use the Product of Powers Property. 

=  (a^{2 + 1})(b^{2 + 1})(c^{3 + 2})

=  (a³)(b³)(c⁵)

=  a³b³c⁵

Problem 7 :

Multiply. 

(4ab)(3a²b²)(2a³b³)

Solution :

=  (4ab)(3a²b²)(2a³b³)

Group factors with like bases together. 

=  (4 ⋅ 3 ⋅ 2)(a ⋅ a² ⋅ a³)(b ⋅ b² ⋅ b³)

Use the Product of Powers Property. 

=  (24)(a^{1 + 2 + 3})(b^{1 + 2 + 3})

=  24a⁶b⁶

Problem 8 :

Multiply. 

(0.5a³b)(a²c²)(6b²)

Solution :

=  (0.5a³b)(a²c²)(6b²)

Group factors with like bases together. 

=  (0.5 ⋅ 1 ⋅ 6)(a³ ⋅ a²)(b ⋅ b²)c²

Use the Product of Powers Property. 

=  3a^{3 + 2}b^{1 + 2}c²

=  3a⁵b³c²

Problem 9 :

Multiply. 

(-3x³y²)(4xy⁵)

Solution :

=  (-3x³y²)(4xy⁵)

Group factors with like bases together. 

=  (-3 ⋅ 4)(x³ ⋅ x)(y² ⋅ y⁵)

Use the Product of Powers Property. 

=  -12x^{3 + 1}y^{2 + 5}

=  -12x⁴y⁷

Problem 10 :

Multiply. 

(-2pq³)(5p²q²)(-3q⁴)

Solution :

=  (-2pq³)(5p²q²)(-3q⁴)

Group factors with like bases together. 

=  (-2 ⋅ 5 ⋅ -3)(p ⋅ p²)(q³ ⋅ q² ⋅ q⁴)

Use the Product of Powers Property. 

=  30p^{1 + 2}q^{3 + 2 + 4}

=  30p³q⁹

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