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## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 3 Algebra Intext Questions

Exercise 3.1

Try These (Text book Page No. 44)

Question 1.

Observe and complete the following table. First one is done for you.

Solution:

Try These (Text book Page No. 46)

Question 1.

Simplify and write the following in exponential form.

1. 2^{3} × 2^{5}

2. p^{2} × P^{4}

3. x^{6} × x^{4}

4. 3^{1} × 3^{5} × 3^{4}

5. (-1)^{2} × (-1)^{3} × (-1)^{5}

Solution:

1. 2^{3} × 2^{5} = 2^{3+5} = 2^{8} [since a^{m} × a^{n} = a^{m+n}]

2. p^{2} × p^{4} = p^{2+4} = p^{6} [since a^{m} × a^{n} = a^{m+n}]

3. x^{6} × x^{4} = x^{6} + 4 = x^{10} [since a^{m} × a^{n} = a^{m+n}]

4. 3^{1} × 3^{5} × 3^{4} = 3^{1+5} × 3^{4} [since a^{m} × a^{n} = a^{m+n}]

= 3^{6} × 3^{4} [since a^{m} × a^{n} = a^{m+n}]

= 3^{10}

5. (-1)^{2} × (-1)^{3} × (-1)^{5}

= (-1)^{2+3} × (-1)^{5} [Since a^{m} × a^{n} = a^{m+n}]

= (-1)^{5} × (-1)^{5}

= (-1)^{5+5} [Since a^{m} × a^{n} = a^{m+n}]

= (-1)^{10}

Try These (Text book Page No. 48)

Question 1.

Simply the following.

1. 23^{5} ÷ 23^{2}

2. 11^{6} ÷ 11^{3}

3. (-5)^{3} ÷ (-5)^{2}

4. 7^{3} ÷ 7^{3}

5. 15^{4} ÷ 15

Solution:

Try These (Text book Page No. 48)

Question 1.

Simplify and write the following in exponent form.

1. (3^{2})^{3}

2. [(-5)^{3}]^{2}

3. (20^{6})^{2}

4. (10^{3})^{5}

Solution:

1. (3^{2})^{3} = 3^{2×3} = 3^{6} [since (a^{m})^{n} = a^{m×n}]

2. [(-5)]^{2} = (-5)^{3×2} = (-5)^{6} [since (a^{m})^{n} = a^{m×n}]

3. (20^{6})^{2} = 20^{6×2} = 20^{12} [since (a^{m})^{n} = a^{m×n}]

4. (10^{3})^{5} = 10^{3×5} = 10^{15} [since (a^{m})^{n} = a^{m×n}]

Question 2.

Express the following exponent numbers using a^{m} × b^{m} = (a × b)^{m}.

(i) 5^{2} × 3^{2}

(ii) x^{3} × y^{3}

(iii) 7^{4} × 8^{4}

Solution:

(i) 5^{2} × 3^{2} = (5 × 3)^{2} = 15^{2} [since a^{m }× b^{m} = (a × b)^{m}]

(ii) x^{3} × y^{3} = (x × y)^{3} = (x y)^{3}

(iii) 7^{4} × 8^{4} = (7 × 8)^{4} = 56^{4}

Question 3.

Simplify the following exponent numbers by using (\(\frac { a }{ b } \))^{m} = \(\frac{a^{m}}{b^{m}}\)

(i) 5^{3} ÷ 2^{3}

(ii) (-2)^{4} ÷ 3^{4}

(iii) 8^{6} ÷ 5^{6}

(iv) 6^{3} ÷ (-7)^{3}

Solution:

(i) 5^{3} ÷ 2^{3} = (\(\frac { 5 }{ 2 } \))^{3} – [Since \(\frac{a^{m}}{b^{m}}\) = (\(\frac { a }{ b } \))^{m}]

(ii) (-2)^{4} ÷ 3^{4} = (\(\frac { -2 }{ 3 } \))^{4}

(iii) 8^{6} ÷ 5^{6} = (\(\frac { 8 }{ 6 } \))^{6}

(iv) 6^{3} ÷ (-7)^{3} = (\(\frac { 6 }{ -7 } \))^{3}

Exercise 3.2

Try These (Text book Page No. 54)

Question 1.

Find the unit digit of the following exponential numbers:

(i) 106^{21}

(ii) 25^{8}

(iii) 31^{18}

(iv) 20^{10}

Solution:

(i) 106^{21} Unit digit of base 106 is 6 and the power is 21 and is positive.

Thus the unit digit of 106^{21} is 6.

(ii) 25^{8} Unit digit of base 25 is 5 and the power is 8 and is positive.

Thus the unit digit of 25^{8} is 5.

(iii) 31^{18} Unit digit of base 31 is 1 and the power 18 and is positive.

Thus the unit digit of 31^{18} is 1.

(iv) 20^{10} Unit digit of base 20 is 0 and the power 10 and is positive.

Thus the unit digit of 20^{10} is 0.

Try These (Text book Page No. 55)

Question 1.

Find the unit digit of the following exponential numbers:

(i) 64^{11}

(ii) 29^{18}

(iii) 79^{19}

(iv) 104^{32}

Solution:

(i) 64^{11} Unit digit of base 64 is 4 and the power is 11 (odd power).

∴ Unit digit of 64^{11} is 4.

(ii) 29^{18} Unit digit of base 29 is 9 and the power is 18 (even power).

Therefore, unit digit of 29^{18} is 1.

(iii) 79^{19} Unit digit of base 79 is 9 and the power is 19 (odd power).

Therefore, unit digit of 7919 is 9.

(iv) 104^{32} Unit digit of base 104 is 4 and the power is 32 (even power).

Therefore, unit digit of 104^{32} is 6.

Exercise 3.3

Try These (Text book Page No. 35)

Question 1.

Complete the following table:

Solution:

Question 2.

Identify the like terms from the following:

(i) 2x^{2}y, 2xy^{2},3xy^{2},14x^{2}y, 7yx

(ii) 3x^{3}y^{2}, y^{3}x, y^{3}x^{2}, – y^{3}x, 3y^{3}x

(iii) 11pq, -pq, 11pqr, -11pq,pq

Solution:

(i) 2x^{2}y, 2xy^{2}, 3xy^{2}, 14x^{2}y, 7yx

(a) 2x^{2}y and 14x^{2}y are like terms.

(b) 2xy^{2} and 3xy^{2} are like terms.

(ii) 3x^{3}y^{2}, y^{3}x, y^{3}x^{2}, – y^{3}x, 3y^{3}x

(a) y^{3}x, – y^{3}x and 3y^{3}x are like terms.

(iii) 11 pq, -pq, 11pqr , -11 pq, pq

(a) 11 pq, -pq, -pq and pq are like terms.