Haryana State Board HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers Ex 13.2 Textbook Exercise Questions and Answers.

## Haryana Board 7th Class Maths Solutions Chapter 13 Exponents and Powers Exercise 13.2

Question 1.

Using laws of exponents, simplify and write the answer in exponential form:

(i) 3^{2} x 3^{4} x 3^{8}

(ii) 6^{15} ÷ 6^{10}

(iii) a^{3} x a^{2}

(iv) 7^{x} x 7^{2}

(v) (5^{2})^{3} ÷ 5^{3}

(vi) 2^{5} x 5^{5}

(vii) a^{4} x b^{4}

(viii) (3^{4})^{3}

(ix) (2^{50} ÷ 2^{15}) x 2^{3}

(x) 8^{t} ÷ 8^{2}

Solution:

(i) 3^{2} x 3^{4} x 3^{8} = 3^{2 + 4 + 8} = 3^{14}

(ii) 6^{15} 6^{10} = \(\frac{6^{15}}{6^{10}}\) = 6^{15 – 10} = 6^{5}

(iii) a^{3} x a^{2} = a^{3+2} = a^{5}

(iv) 7^{x} x 7^{2} = 7^{x+2}

(v) (5^{2})^{3} ÷ 5^{3} = \(\frac{5^{6}}{5^{3}}\) = 5^{6-3} = 5^{3}.

(vi) 2^{5} x 5^{6} = (2 x 5)^{5} = 10^{5}.

(vii) a^{4} x b^{4} = (ab)^{4}.

(viii) (3^{4})^{3} = 3^{4 x 3} = 3^{12}.

(ix) (2^{20} ÷ 2^{15}) x 2^{3} = \(\frac{2^{20}}{2^{15}}\) x 2^{3}

=2^{20-15} x 2^{3}

= 2^{5} x 2^{3} = 2^{5+3} = 2^{8}.

(x) 8^{t} ÷ 8^{2} = \(\frac{8^{t}}{8^{2}}\) = 8^{t-2}.

Question 2.

Simplify and express each of the following in exponential form :

Solution:

(vi) 2° + 3° + 4° = 2°(1 + 2°) + 3° .

(vii) 2° x 3° x 4° = (2 x 3 x 4)° = (24)°.

(viii) (3° + 2°) x 5° = (1 + 1) x 1

= 2 x 1 = 2^{1}.

(xii) (2^{3} x 2)^{2} = 2^{3 x 2} x 2^{2}

= 2^{6} x 2^{2} = 2^{6+2} = 2^{8}

Question 3.

Say true or false and justify your answer:

(i) 10 x 10^{11} = 100^{11}

(ii) 2^{3} x 5^{2}

(iii) 2^{3} x 3^{2} = 6^{5}

(iv) 3^{0} = (1000)^{0}

Solution:

10 x 10^{11} = 100^{11}

= 10^{1 + 11} = 10^{12}

= (10^{2})^{11} = 10^{22}

L.H.S ≠ R.H.S

10 x 10^{11} = 100^{11} is false.

(ii) 2^{3} > 5^{2}

L.H.S. 2^{3} = 8

R.H.S. 5^{2} = 25

∴ 5^{2} > 2^{3}

2^{3} > 5^{2} is false.

(iii) 2^{3} x 3^{2} = 65

L.H.S. 2^{3} x 3^{2}

R.H.S.

6^{5} = (2 x 3)^{5} = 2^{5} x 3^{5}

∴ L.H.S. ≠ R.H.S.

∴ 2^{3} x 3^{2} = 6^{5} is false.

(iv) 3^{0} = (1000)^{0}

L.H.S.

3^{0}

R.H.S.

1000^{0} = (10^{3})^{0}

∴ L.H.S. ≠ R.H.S.

∴ 3^{0} = (1000)^{0} is false.

Question 4.

Express each of the following as a product of prime factor only in exponential form:

(i) 108 x 192

(ii) 270

(iii) 729 x 64

(iv) 768

Solution:

(i) 108 x 192

= 2 x 2 x 3 x 3 x 3 x 2 x 2 x 2 x 2 x 2 x 2 x 3

= 2^{8} x 3^{4}.

(ii) 270

= 2 x 5 x 3 x 3 x 3

= 2 x 5 x 3^{3}.

(iii) 729 x 64

= 3 x 3 x 3 x 3 x 3 x 3 x 2 x 2 x 2 x 2 x 2 x 2

= 3^{6} x 2^{6} = (3 x 2)^{6}.

Question 5.

Simplify :

(i) \(\frac{\left(2^{5}\right)^{2} \times 7^{3}}{8^{3} \times 7}\)

(ii) \(\frac{25 \times 5^{2} \times t^{8}}{10^{3} \times t^{4}}\)

(iii) \(\frac{3^{5} \times 10^{5} \times 25}{5^{7} \times 6^{5}}\)

Solution: