MULTIPLYING MONOMIALS

Problem 1 :

(3x²) (7x³)

Solution :

= (3x²) (7x³)

Multiplying the coefficients and multiplying variables together, we get

= (3 ∙ 7) (x² ∙ x³)

Use the product of power property.

= 21x²⁺³

= 21x⁵

Problem 2 :

8m⁵ ∙ m

Solution :

= 8m⁵ ∙ m

Multiplying the coefficients and multiplying variables together, we get

= (8 ∙ 1) (m⁵ ∙ m¹)

Use the product of power property.

= 8m⁵⁺¹

= 8m⁶

Problem 3 :

t³ ∙ 6t⁷

Solution :

= t³ ∙ 6t⁷

Group factors with like bases together.

= (1 ∙ 6) (t³ ∙ t⁷)

Multiplying the coefficients and multiplying variables together, we get

Use the product of power property.

= 6t³⁺⁷

= 6t¹⁰

Problem 4 :

(4y⁴) (-9y²)

Solution :

= (4y⁴) (-9y²)

Multiplying the coefficients and multiplying variables together, we get

= (4 ∙ -9) (y⁴ ∙ y²)

Use the product of power property.

= - 36y⁴⁺²

= - 36y⁶

Problem 5 :

3r⁵ ∙ 2r² ∙7r⁶

Solution :

= 3r⁵ ∙ 2r² ∙7r⁶

Multiplying the coefficients and multiplying variables together, we get

= (3 ∙ 2 ∙ 7) (r⁵ ∙ r² ∙ r⁶)

Use the product of power property.

= 42r⁵⁺²⁺⁶

= 42r¹³

Problem 6 :

(-2p³r) (11r⁴p⁶)

Solution :

= (-2p³r) (11r⁴p⁶)

Multiplying the coefficients and multiplying variables together, we get

= (-2 ∙ 11) (p³ ∙ p⁶ ∙ r ∙ r⁴)

Use the product of power property.

= -22p ⁽³⁺⁶⁾ r ⁽¹⁺⁴⁾

= -22p⁹r⁵

Problem 7 :

(6y³x) (5y³)

Solution :

= (6y³x) (5y³)

Multiplying the coefficients and multiplying variables together, we get

= (6 ∙ 5) (x ∙ y³ ∙ y³)

Use the product of power property.

= 30xy³⁺³

= 30xy⁶

Problem 8 :

7c⁵a³b ∙ 8a²b⁴c

Solution : 

= 7c⁵a³b ∙ 8a²b⁴c

Multiplying the coefficients and multiplying variables together, we get

= (7 ∙ 8) (a³ ∙ a² ∙ b ∙ b⁴ ∙ c⁵ ∙ c)

Use the product of power property.

= (7 ∙ 8) (a ⁽²⁺³⁾ b ⁽¹⁺⁴⁾ c ⁽⁵⁺¹⁾)

= 56a⁵b⁵c⁶

Problem 9 :

(-3t³u²) (-4u³t)

Solution :

= (-3t³u²) (-4u³t)

Multiplying the coefficients and multiplying variables together, we get

= (-3 ∙ -4) (t³ ∙ t ∙ u² ∙ u³)

Use the product of power property.

= (-3 ∙ -4) (t ⁽³⁺¹⁾ u ⁽²⁺³⁾)

= 12t⁴u⁵

Problem 10 :

9/4 z⁶ × 4/27 z⁷ × 1/2 z²

Solution :

= 9/4 z⁶ × 4/27 z⁷ × 1/2 z²

Multiplying the coefficients and multiplying variables together, we get

= (9/4 ∙ 4/27 ∙ 1/2) (z⁶ ∙ z⁷ ∙ z²)

Use the product of power property.

= 1/6 z ^(6+7+2)

= 1/6 z¹⁵

Problem 11 :

-5/7 q⁴ × -7/5 q⁶

Solution :

= -5/7 q⁴ × -7/5 q⁶

Multiplying the coefficients and multiplying variables together, we get

= (-5/7 ∙ -7/5) (q⁴ ∙ q⁶)

Use the product of power property.

= 1 ∙ q⁴⁺⁶

= q¹⁰

Problem 12 :

6v² × -8v⁷

Solution :

= 6v² × -8v⁷

Group factors with like bases together.

= (6 ∙ -8) (v² ∙ v⁷)

Use the product of power property.

= - 48v²⁺⁷

= - 48v⁹