HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

Haryana State Board HBSE 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions and Answers.

Haryana Board 7th Class Maths Solutions Chapter 13 Exponents and Powers InText Questions

Try These (Page 250)

Question 1.
Find five more such examples, where a number is expressed in exponential form. Also identify the base and the exponent in each case.
Solution:
(i) 64 = 4 × 4 × 4 = 4³
4³ = 4 is the base and 3 is exponent.

(ii) 1625 = 5 × 5 × 5 × 5 = 5⁴
5⁴ = 5 is the base and 4 is the exponent.

(iii) 64= 2 × 2 × 2 × 2 × 2 × 2 = 2⁶
2⁶ = 2 is the base and 6 is the exponent.

(iv) 9 = 3 × 3 = 3²
3² = 3 is the base and 2 is the exponent.

(v) 343 = 7 × 7 × 7 = 7³
7³ = 7 is the base and 3 is exponent.

Try These (Page 251)

Question 1.
Express:
(i) 729 as a power of 3
(ii) 128 as a power of 2
(iii) 343 as a power of 7.
Solution:
(i) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶,
So we can say that 729 = 3⁶.
(ii) 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2
= 2⁷
So we can say that 128 = 27.
(iii) 343 = 7 × 7 × 7 = 7³
So we can say that 343 = 7³.

Try These (Page 254)

Question 1.
Simplify and write in exponential form:
(i) 2⁵ × 2³
(ii) p³ × p²
(iii) 4³ × 4²
(iv) a³ × a² × a⁷
(v) 5³ × 5⁷x 5¹²
(vi) (-4)¹⁰⁰ × (-4)²⁰
Solution:
(i) 2⁵ × 2³ = (2 × 2 × 2 × 2 × 2) x (2 × 2 × 2) = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 2^{5 + 3} = 2⁸.

(ii) p³ × p² = (p × p × p) × (p × p)
= p³⁺² = p⁵

(iii) 4³ × 4² = (4 × 4 × 4) × (4 × 4)
= 4^{3 + 2} = 4⁵

(iv) a³ × a² × a⁷ = a × a × a × a × a × a × a × a × a × a × a × a = a^{3 + 2 + 7} = a¹².

(v) 5³ × 5⁷x 5¹²
= 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5¹²
= 5^{3 + 7 + 12} = 5²²

(vi) (-4)¹⁰⁰ × (-4)²⁰
= 4¹⁰⁰ × (-4)²⁰ = 4¹²⁰.

Try These (Page 255)

Question 1.
Simplify and write in exponential: 11⁶ 4-11² = 11⁴.
(i) 2⁹ ÷ 2³
(ii) 10⁸ ÷ 10⁴
(iii) 9¹¹ ÷ 9⁷
(iv) 20¹⁵ ÷ 20¹³
(v) 7¹³ ÷ 7¹⁰
Solution:
(i) 29 ÷ 23 = 2^9-3 = 2⁶
(ii) 10⁸ ÷ 10⁴ = 10^8-4 = 10^8-4
(iii) 9¹¹ ÷ 9⁷ = 9^11-7 = 9⁴
(iv) 20¹⁵ ÷ 20¹³ = 20^15-13 = 20²
(v) 7¹³ ÷ 7¹⁰= 7^13-10 = 7³

Try These (Page 255)

Question 1.
Simplify and write the answer in exponential form :
(i) (6²)⁴
(ii) (2²)¹⁰⁰
(iii) (7⁵⁰)²
(iv) (5³)⁷
Solution:
(i) (6²)⁴ = 6^2×4 = 6⁸.
(ii) (2²)¹⁰⁰
= 2^{2 × 100} = 2²⁰⁰.
(iii) (7⁵⁰)² = 7 ^{50 × 2} = 7¹⁰⁰.
(iv) (5³)⁷ = 53^{3 × 7} = 5²¹.

Try These (Page 256)

Question 1.
Put into another form using a^m × b^m = (ab)^m
(i) 4³ × 2³
(ii) 2⁵ × b⁵
(iii) a² × t²
(iv) 5⁶ × (-2)⁶
(v) (- 2)⁴ × (- 3)⁴
Solution:
(i) 4³ × 2³ = (4 × 2)³ = 8³.
(ii) 2⁵ × b⁵ = (2 × b)⁵ = (2b)5.
(iii) a² × t² = (ax t)² = (at)².
(iv) 5⁶ × (-2)⁶ = [5 × (- 2)]⁶ = (- 10)⁶.
(v) (- 2)⁴ × (- 3)⁴= [(- 2) × (- 3)]⁴ = (6)⁴.

Try These (Page 257)

Question 1.
Put into another form using
a^m b^m = \(\left(\frac{a}{b}\right)^{m}\)
(i) 4⁵ ÷ 3⁵
(ii) 2⁵ ÷ b⁵
(iii) (-2)³ ÷ b⁵
(iv) p⁴ ÷ q⁴
(v) 5⁶ ÷ (-2)⁶
Solution:

Try These (Page 261)

Question 1.
Expand by expressing powers of 10 in the exponential form :
(i) 172
(ii) 5,643
(iii) 56,439
(iv) 176,428
Solution:
(i) 172 = 1 × 100 + 7 × 10 + 2
= 10² + 6 × 10¹ + 2 × 10⁰.

(ii) 5,643 = 5 × 1000 + 6 × 100 + 4 × 10 + 3
5 × 10³ + 6 × 10² + 4 × 10¹ + 3 × 10⁰.

(iii) 56, 439 = 5 × 10000 + 6 × 1000 + 4 × 100 + 3 × 10 + 9
= 5 × 10⁴ + 6 × 10³ + 4 × 10² + 3 × 10 + 9 × 10⁰

(iv) 176,428
= 1 × 100000 + 7 × 10000 + 6 × 1000 + 4 × 100 + 2 × 10 + 8
= 1 × 10⁶ + 7 × 10⁴ + 6 × 10³ + 4 × 10² + 2 × 10 + 8 × 10°.