Question 1: Find each of the following product:
5x2 × 4x3
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:
−3a2 × 4b4
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:
(−5xy) × (−3x2yz)
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 x3y2z216x3y2z2.
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:
(7ab) × (−5ab2c) × (6abc2)
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:
(−5a) × (−10a2) × (−2a3)
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:
(−4x2) × (−6xy2) × (−3yz2)
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)×(−6xy2)×(−3yz2)={(−4)×(−6)×(−3)}×(x2×x)×(y2×y)×z2={(−4)×(−6)×(−3)}×(x2+1)×(y2+1)×z2=−72x3y3z2Thus, the answer is −72x3y3z2-72x3y3z2.
Question 12: Find each of the following product:

Answer 12: 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:

×(a4×a2)×(b×b2)
×a4+2×b1+2
×a6×b3
=− 3/5 a6b3
Thus, the answer is − 3/5 a6b3
Question 13: Find each of the following product:

Answer 13: 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:

×(a×a×a2)×(b2×b)×(c2×c)
×(a×a×a2)×(b2×b)×(c2×c)
×(a1+1+2)×(b2+1)×(c2+1)
=−a4b3c3
Thus, the answer is −a4b3c3-a4b3c3.
Question 14: Find each of the following product:

Answer 14: 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:
(4/3 u2vw)×(−5uvw2)×(1/3 v2wu)
×(u2×u×u)×(v×v×v2)×(w×w2×w)
×(u2+1+1)×(v1+1+2)×(w1+2+1)
=− 20/9 u4v4w4
Thus, the answer is − 20/9 u4v4w4
Question 15: Find each of the following product:
(0.5x)×(1/3 xy2z4)×(24x2yz)0.5x×13xy2z4×24x2yz
Answer 15: 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:
(0.5x)×(1/3 xy2z4)×(24x2yz)
=(0.5×1/3×24)×(x×x×x2)×(y2×y)×(z4×z)
=(0.5×1/3×24)×(x1+1+2)×(y2+1)×(z4+1)
=4x4y3z5
Thus, the answer is 4x4y3z54x4y3z5.
Question 16: Find each of the following product:
(4/3 pq2)×(−1/4 p2r)×(16p2q2r2)43pq2×-14p2r×16p2q2r2
Answer 16: 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:
(4/3 pq2)×(−1/4 p2r)×(16p2q2r2)
={4/3×(−1/4)×16}×(p×p2×p2)×(q2×q2)×(r×r2)
={4/3×(− 1/4)×16}×(p1+2+2)×(q2+2)×(r1+2)
=− 16/3p5q4r3
Thus, the answer is −1/3 p5q4r3-13p5q4r3.
Question 17: Find each of the following product:
(2.3xy) × (0.1x) × (0.16)
Answer 17: 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:
(2.3xy)×(0.1x)×(0.16)=(2.3×0.1×0.16)×(x×x)×y=(2.3×0.1×0.16)×(x1+1)×y=0.0368x2yThus, the answer is 0.0368x2y0.0368x2y.
Question 18: Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)
Answer 18: We have to find the product of the expression in order to express it as a monomial.
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:
(3x)×(4x)×(−5x)={3×4×(−5)}×(x×x×x)={3×4×(−5)}×(x1+1+1)=−60x33x×4x×-5x=3×4×-5×x×x×x=3×4×-5×x1+1+1=-60x3
Substituting x = 1 in LHS, we get:
LHS =(3x)×(4x)×(−5x)=(3×1)×(4×1)×(−5×1)
=−60
Putting x = 1 in RHS, we get:
RHS =−60x3=−60(1)3=−60×1=−60∵∵ LHS = RHS for x = 1; therefore, the result is correct
Thus, the answer is −60x3-60x3.
Question 19: Express each of the following product as a monomials and verify the result in each case for x = 1:
(4x2) × (−3x) × (4/5 x3)
Answer 19: We have to find the product of the expression in order to express it as a monomial.
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)×(−3x)×(4/5 x3)
={4×(−3)×4/5}×(x2×x×x3)
={4×(−3)×4/5}×(x2+1+3)
=− 48/5x6
∴∴ (4x2)×(−3x)×(4/5 x3)=− 48/5x6
Substituting x = 1 in LHS, we get:
LHS=(4x2)×(−3x)×(4/5 x3)
=(4×12)×(−3×1)×(4/5 ×13)
=4×(−3)×4/5
=−48/5
Putting x = 1 in RHS, we get:
RHS=− 48/5 x6
=−48/5×16
=−48/5
∵∵ LHS = RHS for x = 1; therefore, the result is correct
Thus, the answer is − 48/5 x6-485x6.
Question 20: Express each of the following product as a monomials and verify the result in each case for x = 1:
(5x4) × (x2)3 × (2x)2
Answer 20: We have to find the product of the expression in order to express it as a monomial.
To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e., am×an=am+n and (am)n=amn am×an=am+n and amn=amn .
We have:
(5x4)×(x2)3×(2x)2 =(5x4)×(x6)×(22×x2)=(5×22)×(x4×x6×x2)=(5×22)×(x4+6+2)=20x12∴ (5x4)×(x2)3×(2x)2 =20x12
Substituting x = 1 in LHS, we get:
LHS=(5x4)×(x2)3×(2