RBSE Solutions for Class 7 Maths Chapter 13 Exponents and Powers Intext Questions

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 13 Exponents and Powers Intext Questions Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 13 Exponents and Powers Intext Questions

(Try These Page No: 251)

Question 1.
Express:
(i) 729 as a power of 3;
Answer:
729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶

(ii) 128 as a power of 2;
Answer:
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷

(iii) 343 as a power of 7.
Answer:
343 = 7 × 7 × 7 = 7³

(Try These: Page No: 254)

Question 1.
Simplify and write in exponential form:
(i) 2⁵ × 2³
(ii) p³ × p²
(iii) 4³ × 4²
(iv) a³ × a² × a⁷
(v) 5³ × 5⁷ × 5¹²
(vi) (- 4)¹⁰⁰ × (- 4)²⁰
Answer:
Applying laws of exponents am × an = am+n
(i) 2⁵ × 2³ = 2^{5 + 3} = 2⁸
(ii) p³ × p² = p^{3 + 2} = p⁵
(iii) 4³ × 4² = 4^{3 + 2} = 4⁵
(iv) a³ × a² × a⁷ = a^{3 + 2 + 7} = a¹²
(v) 5³ × 5⁷ × 5¹² = 5^{3 + 7 + 12} = 5²²
(vi) (- 4)¹⁰⁰ × (- 4)²⁰ = (- 4)^{100 + 20} = (- 4)¹²⁰

(Try These Page No: 255)

Question 1.
Simplify and write in exponential form:
(i) 2⁹ ÷ 2³
(ii) 10⁸ ÷ 10⁴
(iii) 9¹¹ ÷ 9⁷
(iv) 20¹⁵ ÷ 20¹³
(v) 7¹³ ÷ 7¹⁰
Answer:
Applying laws of exponents
a^m ÷ aⁿ = a^{m - n}
(i) 2⁹ ÷ 2³ = 2^{9 - 3} = 2⁶
(ii) 10⁸ ÷ 10⁴ = 10^{8 - 4} = 10⁴
(iii) 9¹¹ ÷ 9⁷ = 9^{11 - 7} = 9⁴
(iv) 20¹⁵ ÷ 20¹³ = 2^{15 - 13} = 20²
(v) 7¹³ ÷ 7¹⁰ = 7^{13 - 10} = 7³

(Try These Page No: 255)

Question 1.
Simplify and write the answer in exponential form:
(i) (6²)⁴
(ii) (2²)¹⁰⁰
(iii) (7⁵⁰)²
(iv) (5³)⁷
Answer:
Applying laws of exponents (a^m)ⁿ = a^mn
(i) (6²)² = 6^{2 × 4} = 6⁸
(ii) (2²)¹⁰⁰ = 2^{2 × 100} = 2²⁰⁰
(iii) (7⁵⁰)² = 7^{50 × 2} = 7¹⁰⁰
(iv) (5³)⁷ = 5^{3 × 7} = 5²¹

(Try These Page No: 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
Answer:
Applying laws of exponents a^m × b^m = (ab)^m
(i) 4³ × 2³ = (4 × 2)³ = 8³
(ii) 2⁵ × b⁵ = (2 × b)⁵ = (2b)⁵
(iii) a² × t² = (a × 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 No: 257)

Question 1.
Put into another form using
a^m ÷ b^m = \(\left(\frac{a}{b}\right)^{m}\)
(i) 4⁵ ÷ 3⁵
Answer:
4⁵ ÷ 3⁵ = \(\left(\frac{4}{3}\right)^{5}\)

(ii) 2⁵ ÷ b⁵
Answer:
2⁵ ÷ b⁵ = \(\left(\frac{2}{b}\right)^{5}\)

(iii) (- 2)³ ÷ b³
Answer:
(- 2)³ ÷ b³ = \(\left(\frac{-2}{b}\right)^{3}\)

(iv) p⁴ ÷ q⁴
Answer:
p⁴ ÷ q⁴ = \(\left(\frac{p}{q}\right)^{4}\)

(v) 5⁶ ÷ (-2)⁶
Answer:
5⁶ ÷ (-2)⁶ = \(\left(\frac{5}{-2}\right)^{6}=\left(\frac{5}{2}\right)^{6}\)

(Try These Page No: 261)

Question 1.
Expand by expressing powers of 10 in the exponential form: '
(i) 172
Answer:
172
Here, 172 =100 + 70 + 2
= 1 × 100 + 7 × 10 + 2 × 1
= 1 × 10² + 7 × 10¹ + 2 × 10⁰

(ii) 5,643
Answer:
5,643
Here, 5,643 = 5000 + 600 + 40 + 3
= 5 × 1000 + 6 × 100 + 4 × 10 + 3 × 1
= 5 × 10³ + 6 × 10² + 4 × 10¹ + 3 × 10⁰

(iii) 56,439
Answer:
56,439
Here, 56,439 = 50000 + 6000 + 400 + 30 + 9
= 5 × 10000 + 6 × 1000 + 4 × 100 + 3 × 10 + 9× 1
= 5 × 10⁴ + 6 × 10³ + 4 × 10² + 3 × 10¹ + 9 × 10⁰

(iv) 1,76,428
Answer:
1,76,428
Here, 1,76,428 = 100000 + 70000 + 6000 + 400 + 20 + 8
= 1 × 100000 + 7 × 10000 + 6 × 1000 + 4 × 100 + 2 × 10 + 8 × 1
= 1 × 10⁵ + 7 × 10⁴ + 6 × 10³ + 4 × 10² + 2 × 10² + 8 × 10⁰