RBSE Solutions for Class 8 Maths Chapter 12 Exponents and Powers Intext Questions

Rajasthan Board RBSE Solutions for Class 8 Maths Chapter 12 Exponents and Powers Intext Questions Textbook Exercise Questions and Answers.

RBSE Class 8 Maths Solutions Chapter 12 Exponents and Powers Intext Questions

(Page No: 193)

Question 1.
What is 10^-10 equal to?
Answer:
For any none zero number a and a positive integer n,
We define a^-n = \(\frac{1}{a^{n}}\)
∴ 10^-10 = \(\frac{1}{10^{10}}\)

(Try These Page No: 194)

Question 1.
Find the multiplicative inverse of the following :
(i) 2^-4
(ii) 10^-5
(iii) 7^-2
(iv) 5^-3
(v) 10^-100
Answer:
We know that multiplicative inverse of a is \(\frac{1}{a}\). Therefore,
(i) The multiplicative inverse of
2^-4 = \(\frac{1}{2^{-4}}\) = 2⁴

(ii) The multiplicative inverse of
10^-5 = \(\frac{1}{10^{-5}}\) = 10⁵

(iii) The multiplicative inverse of
7^-2 = \(\frac{1}{7^{-2}}\) = 7²

(iv) The multiplicative inverse of
5^-3 = \(\frac{1}{5^{-3}}\) = 5³

(v) The multiplicative inverse of
10^-100 = \(\frac{1}{10^{-100}}\) = 10¹⁰⁰

(Try These Page No: 194)

Question 1.
Expand the following numbers using exponents:
(i) 1025.63
(ii) 1256.249
Answer:
(i) 1025.63
= 1 × 1000 + 2 × 10 + 5 × 1 + \(\frac{6}{10}\) + \(\frac{3}{100}\)
= 1 × 10³ + 2 × 10 + 5 × 1 + 6 × 10^-1 + 3 × 10^-2

(ii) 1256.249
= 1 × 1000 + 2 × 100 + 5 × 10 + 6 × 1 + 2 × \(\frac{1}{10}\) + 4 × \(\frac{1}{100}\) + 9 × \(\frac{1}{1000}\)
= 1 × 10³ + 2 × 10² + 5 × 10 + 6 × 1 + 2 × 10^-1 + 4 × 10^-2 + 9 × 10^-3

(Try These Page No: 195)

Question 1.
Simplify and write in exponential form—
(i) (- 2)^-3 × (- 2)^-4
Answer:
We know that if a is any non-zero integer and m, n are integers, then a^m × aⁿ = a^{m + n}
(- 2)^-3 × (- 2)^-4 = (- 2)^{(-3) + (- 4)} = (- 2)^-7
= \(\frac{1}{(-2)^{7}}\) = \(\frac{1}{(-1)^{7} \times(2)^{7}}\)
= \(\frac{1}{-1 \times(2)^{7}}\) = -\(\frac{1}{2^{7}}\)

(ii) p³ × p^-10
Answer:
p³ × p^-10 = p^{3 - 10} = p^-7 = \(\frac{1}{p^{7}}\)

(iii) 3² × 3^-5 × 3⁶
Answer:
3² × 3^-5 × 3⁶ = 3^{2 - 5 + 6} = 3³

(Try These Page No: 198)

Observe the following facts.
1. The distance from the Earth to the Sun is 149,600,000,000 m.
2. The speed of light is 300,000,000 m/sec.
3. Thickness of Class VII Mathematics book is 20 mm.
4. The average diameter of a Red Blood Cell is 0.000007 mm.
5. The thickness of human hair is in the range of 0.005 cm to 0.01 cm.
6. The distance of moon from the Earth is 384,467,000 m (approx).
7. The size of a plant cell is 0.00001275 m.
8. Average radius of the Sun is 695000 km.
9. Mass of propellant in a space shuttle solid rocket booster is 503600 kg.
10. Thickness of a piece of paper is 0.0016 cm.
11. Diameter of a wire on a computer chip is 0.000003 m.
12. The height of Mount Everest is 8848 m. Identify very large and very small numbers from the above facts and write them in the adjacent table:

Answer:

(Try These Page No: 199)

Question 1.
Write the following numbers in standard form—
(i) 0.000000564
(ii) 0.0000021
(iii) 21600000
(iv) 15240000
Answer:
(i) 0.000000564 = \(\frac{564}{1000000000}\) = \(\frac{564}{10^{9}}\)
= \(\frac{5.64 \times 100}{10^{9}}\)
= 5.64 × 10² × 10^-9
= 5.64 × 10^-7

(ii) 0.0000021 = \(\frac{21}{10000000}\) = \(\frac{21}{10^{7}}\)
= \(\frac{2.1 \times 10}{10^{7}}\) = 2.1 × 10 × 10^-7
= 2.1 × 10^-6

(iii) 21600000= 216 × 10⁵ = 2.16 × 100 × 10⁵
= 2.16 × 10² × 10⁵ = 2.16 × 10⁷

(iv) 15240000= 1524 × 10⁴
= 1.524 × 1000 × 10⁴
= 1.524 × 10³ × 10⁴
= 1.524 × 10⁷

Question 2.
Write all the facts given in the standard form. (Page 199)
Answer:
All the facts given in the standard form are as below :
(1) The distance from the Earth to the Sun is
149,600,000,000 m = 1.496 × 10¹¹ m

(2) The speed of light is 300,000,000 m/sec
= 3 × 10⁸ m/sec

(3) Thickness of class VII Mathematics book
is = 20 mm = 2 × 10¹ mm

(4) The average diameter of a Red Blood Cell is = 0.000007 mm
= 7 × 10^-6 mm

(5) The thickness of human hair is in the range of 0.005 cm to 0.01 cm
= 5 × 10^-3 cm to 1 × 10^-2 cm

(6) The distance of moon from the Earth is 384,467,000 m (approx.)
= 3.84467 × 10⁸ m

(7) The size of a plant cell is 0.00001275 m
= 1.275 × 10⁵ m

(8) Average radius of the Sun = 695000 km
= 6.95 × 10⁵ km

(9) Mass of propellant in a space shuttle socid rocket booster = 503600 kg
= 5.036 × 10⁵ kg

(10) Thickness of a piece of paper
= 0.0016 cm = 1.6 × 10^{- 3} cm

(11) Diameter of a wire on a computer chip
= 0.000003 m = 3 × 10^-6 m

(12) The height of Mount Everest
= 8848 m = 8.848 × 10³ m