**Exercise 6.3**

** Find each of the following products: **

**1. 5x**^{2} × 4x^{3}

^{2}× 4x

^{3}

**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:

5x^{2} × 4x^{3}

= (5×4)×(x2×x3)

= 20×5 (∵a^{m }× a^{n} = a^{m}^{+}^{n})

Thus, the answer is 20×5.

**2. −3a2×4b4**

**Solution:**

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

We have:

−3a^{2}×4b^{4}

= (−3×4) × (a^{2}×b^{4})

= −12a^{2}b^{4}

Thus, the answer is −12^{a}2b^{4}.

**3. (−5xy) × (−3x2yz)**

** Solution:**

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

We have:

(−5xy) × (−3x^{2}yz)

= [(−5) × (−3)] × (x×x^{2}) × (y×y)×z

= 15×(x^{1}^{+}^{2}) × (y^{1}^{+}^{1})×z

= 15x^{3}y^{2}z

Thus, the answer is 15x^{3}y^{2}z.

** ****Solution: **

** **To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, that is, a^{m}×a^{n}=a^{m}^{+}^{n}

We have:

** **

**Solution:**

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, that is, am×an=am+n

We have:

**Solution:**

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, that is, a^{m}×a^{n}=a^{m}^{+}^{n}

We have:

**Solution:**

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, that is, a^{m}×a^{n}=a^{m}^{+}^{n}

We have:

**Solution:**

To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, that is, a^{m}×a^{n}=a^{m}^{+}^{n}

**Find each of the following products:**

**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 }× a^{n} = a^{m + n}, wherever applicable.

We have:

**10. Find the products**

**(−5a) × (−10a**^{2}) × (−2a^{3}

^{2}) × (−2a

^{3}

**Solution:**

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

We have:

**11. Find the products**

**(−4×2) × (−6xy2) × (−3yz2)**

**Solution:**

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

We have:

**12. Find the products**

** **

**17. Find the products**

**(2.3xy) × (0.1x) × (0.16)**

**Solution:**

^{m }× a^{n} = 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) × (x^{1+1}) × y

= 0.0368x^{2}y

Thus, the answer is 0.0368x^{2}y.

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

**(3x) × (4x) × (−5x)**

**Solution:**

**19. Express each of the following products as a monomials and verify the result in each case for x = 1: **

** **

**Solution:**

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

**We have:**