**Chapter 6: Algebraic Expressions and Identities Exercise – 6.3**

**Question: 1**

Find products

5x^{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:

**Question: 2**

Find products

−3a^{2} × 4b^{4}

**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:

**Question: 3**

Find products

(−5xy) × (−3x^{2}yz)

**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:

**Question: 4**

Find products

**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:

**Question: 5**

Find products

**Solution:**

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

We have:

**Question: 6**

Find products

**Solution:**

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

We have:

**Question: 7**

Find products

**Solution:**

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

We have:

**Question: 8**

Find products

**Solution:**

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

We have:

**Question: 9**

Find the products

(7ab) × (− 5ab^{2}c) × (6abc^{2})

**Solution:**

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

We have:

**Question: 10**

Find the products

(−5a) × (−10a^{2}) × (−2a^{3})

**Solution:**

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

We have:

**Question: 11**

Find the products

(−4x^{2}) × (−6xy^{2}) × (−3yz^{2})

**Solution:**

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

We have:

**Question: 13**

Find the products

**Solution:**

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

We have:

**Question: 14**

Find the products

**Solution:**

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

We have:

**Question: 15**

Find the products

**Solution:**

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

We have:

**Question: 16**

Find the products

**Solution:**

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

We have:

**Question: 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.

**Question: 18**

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

(3x) × (4x) × (−5x)

**Solution:**

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

We have:

**Question: 19**

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

**Solution:**

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

We have:

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

Thus, the answer is – (48/5) x^{6}.

**Question: 20**

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

(5x^{4}) × (x^{2})^{3} × (2x)^{2}

**Solution:**

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

We have:

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

Thus, the answer is 20x^{12}

**Question: 21**

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

(x^{2})^{3} × (2x) × (−4x) × (5)

**Solution:**

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

We have:

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

Thus, the answer is -40x^{8}

**Question: 22**

Write down the product of −8x^{2}y^{6} and −20xy. Verify the product for x = 2.5, y = 1.

**Solution:**

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

We have:

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

Thus, the answer is −160x^{3}y^{7}

**Question: 23**

Evaluate (3.2x 6y^{3}) × (2.1x^{2}y^{2}) when x = 1 and y = 0.5.

**Solution:**

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

We have:

**Question: 24**

Find the value of (5x^{6}) × (−1.5x^{2}y^{3}) × (−12xy^{2}) when x = 1, y = 0.5.

**Solution:**

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

We have:

**Question: 25**

Evaluate when (2.3a^{5}b^{2}) × (1.2a^{2}b^{2}) when a = 1 and b = 0.5.

**Solution:**

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

We have:

**Question: 26**

Evaluate for (−8x^{2}y^{6}) × (−20xy) x = 2.5 and y = 1

**Solution:**

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

We have:

**Question: 27**

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

(-xy^{3}) × (yx^{3}) × (xy)

**Solution:**

^{m }× a^{n} = 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:**

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

We have:

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

Thus, the answer is (5/32)x^{7}y^{7}.

**Question: 29**

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

**Solution:**

** **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:

**Question: 30**

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

**Solution:**

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

We have:

**Question: 31**

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

**Solution:**

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

We have:

**Question: 32**

Evaluate of the following when x = 2, y = -1.

**Solution:**

** **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:

**Question: 33**

Evaluate of the following when x = 2, y = -1.

**Solution:**

** **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: