Chapter 6: Algebraic Expressions and Identities Exercise – 6.3

Question: 1

Find products

5x² × 4x³

Solution:

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices. However, use of these laws is subject to their applicability in the given expressions. In the present problem, to perform the multiplication, we can proceed as follows:

 

Question: 2

Find products

−3a² × 4b⁴

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 3

Find products

(−5xy) × (−3x²yz)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 4

Find products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 5

Find products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 6

Find products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 7

Find products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 8

Find products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 9

Find the products

(7ab) × (− 5ab²c) × (6abc²)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 10

Find the products

(−5a) × (−10a²) × (−2a³)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 11

Find the products

(−4x²) × (−6xy²) × (−3yz²)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 12

Find the products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m× aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 13

Find the products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 14

Find the products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 15

Find the products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 16

Find the products

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 17

Find the products

(2.3xy) × (0.1x) × (0.16)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

(2.3xy) × (0.1x) × (0.16)

= (2.3 × 0.1 × 0.16) × (x × x) × y

= (2.3 × 0.1 × 0.16) × (x¹⁺¹) × y

= 0.0368x²y

Thus, the answer is 0.0368x²y.

 

Question: 18

Express the products as a monomials and verify the result for x = 1

(3x) × (4x) × (−5x)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 19

Express the products as a monomials and verify the result for x = 1

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

Since, LHS = RHS for x = 1; therefore, the result is correct

Thus, the answer is – (48/5) x⁶.

 

Question: 20

Express the products as a monomials and verify the result for x = 1

(5x⁴) × (x²)³ × (2x)²

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

Since, LHS = RHS for x = 1; therefore, the result is correct

Thus, the answer is 20x¹²

 

Question: 21

Express the products as a monomials and verify the result for x = 1

(x²)³ × (2x) × (−4x) × (5)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

Since, LHS = RHS for x = 1; therefore, the result is correct

Thus, the answer is -40x⁸

 

Question: 22

Write down the product of −8x²y⁶ and −20xy. Verify the product for x = 2.5, y = 1.

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

Because LHS is equal to RHS, the result is correct.

Thus, the answer is −160x³y⁷

 

Question: 23

Evaluate (3.2x 6y³) × (2.1x²y²) when x = 1 and y = 0.5.

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 24

Find the value of (5x⁶) × (−1.5x²y³) × (−12xy²) when x = 1, y = 0.5.

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 25

Evaluate when (2.3a⁵b²) × (1.2a²b²) when a = 1 and b = 0.5.

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 26

Evaluate for (−8x²y⁶) × (−20xy) x = 2.5 and y = 1

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 27

Express the products as a monomials and verify the result for x = 1, y = 2

(-xy³) × (yx³) × (xy)

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

 

Question: 28

Express the products as a monomials and verify the result for x = 1, y = 2

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have:

Because LHS is equal to RHS, the result is correct.

Thus, the answer is (5/32)x⁷y⁷.

 

Question: 29

Express the products as a monomials and verify the result for x = 1, y = 2

Solution:

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, a^m × aⁿ = a^m + n, wherever applicable.

We have: