MULTIPLYING MONOMIALS

To multiply two or more monomials, we have to follow the rule given below.

(i) Multiply the signs

(ii) Multiply the coefficients

(iii) Multiply the variables.

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

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