**Question 1: ***Find each of the following product:*

5*x*^{2}^{ }× 4*x*^{3}

**Answer 1: To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices. However, use of these laws are subject to their applicability in the given expressions.**

In the present problem, to perform the multiplication, we can proceed as follows:

5x2×4x3=(5×4)×(x2×x3)5x2×4x3=5×4×x2×x3

=20x5=20x5 (∵∵ am×an=am+nam×an=am+n)

Thus, the answer is 20x520x5.

**Question 2: ***Find each of the following product:*

−3*a*^{2} × 4*b*^{4}

**Answer 2:** To multiply algebraic expressions, we can use commutative and associative laws along with the law of indices, am×an=am+nam×an=am+n, wherever applicable.

We have:

−3a2×4b4=(−3×4)×(a2×b4)=−12a2b4-3a2×4b4=-3×4×a2×b4=-12a2Thus, the answer is −12a2b4-12a2b4.

**Question 3: ***Find each of the following product:*

(−5*xy*) × (−3*x*^{2}*yz*)

**Answer 3:** To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, am×an=am+nam×an=am+n, wherever applicable.

We have:

(−5xy)×(−3x2yz)={(−5)×(−3)}× (x×x2)×(y×y)×z=15× (x1+2)×(y1+1)×z=15x3y2z-5xy×-3x2yz=-5×-3× x×x2×y×y×z=15× x1+2×y1+1×z=15x3y2Thus, the answer is 15x3y2z15x3y2z.

**Question 4: ***Find each of the following product:*

**Answer 4: To multiply algebraic expressions, we use commutative and associative laws along with the the law of indices, that is, am×an=am+nam×an=am+n. **

**We have: **

**Thus, the answer is 1/6 ****x****3y2z216x3y2z2. **

**Question 5: ***Find each of the following product:*

**Answer 5: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n. **

**We have: **

** (x×x2)×(y2×y)×(z×z2) **

** ×(x1+2)×(y2+1)×(z1+2) **

**= **- 91/15 x3y3x3

Thus, the answer is **= **- 91/15 x3y3x3

**Question 6: ****Find each of the following product:**

**Answer 6: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n. **

**We have: **

** ×(x3×x)×(z×z2)×y **

** ×(x3+1)×(z1+2)×y **

**= 9/10 x4yz3=910x4yz3 **

**Thus, the answer is 9/10 x4yz3=910x4yz3 **

**Question 7: ***Find each of the following product:*

**Answer 7:To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.**

We have:

** **

** (a2×a3)×(b2×b2)×c2 **

(a2+3)×(b2+2)×c2

= - 1/6 a5b4c2

Thus, the answer is = - 1/6 a5b4c2

**Question 8: ****Find each of the following product: **

**Answer 8: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.**

We have:

=(−7×1/4)×(x×x2)×(y×y)×z

=(−7×1/4)×(x1+2)×(y1+1)×z

=− 7/4 x3y2z

Thus, the answer is − 7/4 x3y2z

**Question 9: ***Find each of the following product:*

(7*ab*)* ×* (−5*ab*^{2}*c*) *×* (6*abc*^{2})

**Answer 9: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.**

We have: (7ab)×(−5ab2c)×(6abc2)={7×(−5)×6}×(a×a×a)×(b×b2×b)×(c×c2)={7×(−5)×6}×(a1+1+1)×(b1+2+1)×(c1+2)=−210a3b4c3 Thus, the answer is −210a3b4c3-210a3b4c3.

**Question 10: ***Find each of the following product:*

(−5*a*) × (−10*a*^{2}) × (−2*a*^{3})

**Answer 10: To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.**

We have:

(−5a)×(−10a2)×(−2a3)={(−5)×(−10)×(−2)}×(a×a2×a3)={(−5)×(−10)×(−2)}×(a1+2+3)=−100a6Thus, the answer is −100a6-100a6.

**Question 11: ***Find each of the following product:*

(−4*x*^{2}) × (−6*xy*^{2}) × (−3*yz*^{2})

**Answer 11:** To multiply algebraic expressions, we use commutative and associative laws along with the law of indices, i.e., am×an=am+nam×an=am+n.

We have:

(−4x2)×(−6x