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

Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 12 Exponents and Powers Intext Questions and Answers.

Gujarat Board Textbook Solutions Class 8 Maths Chapter 12 Exponents and Powers

Try These (Page 194)

Question 1.
Find the multiplicative inverse of the following?

1. 2^-4
2. 10^-5
3. 7^-2
4. 5^-3
5. 100^-100

Solution:

1. The multiplicative inverse of 2^-4 is 2⁴ ponents.
2. The multiplicative inverse of 10^-5 is 10⁵
3. The multipicative inverse of 7^-2 is 7²
4. The multipicative inverse of 5^-3 is 5²
5. The multipicative inverse of 10^-100 is 10¹⁰⁰

Try These (Page 194)

Question 1.
Expand the following number using exponents?
(i) 1025.63
(ii) 1256.249
Solution:

Try These (Page 195)

Question 1.
Simpfy and write in exponential form?

1. (-2)^-3 × (-2)^-4
2. p³ × p^-10
3. 3² × 3^-5 × 3⁶

Solution:
1. (-2)³ × (-2)^-4 = (-2)^(-3)+(-4) [∵a^m × aⁿ]
= (-2)^-7 or \(\frac{1}{(-2)^{7}}\)

2. p³ × p^-10 = (p)^3+(-10) = (p)^-7 or \(\frac{1}{(10)^{7}}\)

3. 3² × 3^-5 × 3⁶ = 3^2+(-5)+6 = 3^8-5 = 3³

Law II: \(\frac{a^{m}}{a^{n}}\) = a^m-n
Example: 5^-1 + 5^-2 = 5^-1-(-2) = 5^-1+2 = 5¹ or 5

Law III: (a^m)ⁿ = a^mn
Example: (9^-1)^-3 = 9^(-1)×(-3) = 9³

Law IV: a^m × b^m = (ab)^m
Example: 2^-4 × 3^-4 = (2 × 3)^-4 = 6^-4 or \(\frac{1}{6^{4}}\)

Law V: \(\frac{a^{m}}{b^{m}}=\left(\frac{a}{b}\right)^{m}\)
Example: \(\frac{3^{-5}}{7^{-5}}\) = \(\frac{3}{7}\)^-5 or \(\frac{7}{3}\)⁵

Law VI: a⁰ = 1
Example:
(i) (-38)⁰ = 1
(ii) (32456)⁰ = 1

Try These (Page 199)

Question 1.
Write the following numbers in standard form?

1. 0.000000564
2. 0.0000021
3. 15240000

Solution:
1. 0.000000564 = \(\frac{564}{1000000000}\)
= \(\frac{5.64}{10^{9}} \times 10^{2}\)
= \(\frac{5.64}{10^{7}}\)
= 5.64 × 10^-7

2. 0.0000021 = \(\frac{21}{10000000}\)
= \(\frac{2.1 \times 10}{10000000}=\frac{2.1}{1000000}\)
= 2.1 × 10^-6
∴ 0.0000021 = 2.1 × 10^-6

3. 15240000 = 1524 × 1000
= 1.524 × 1000 × 1000
= 1.524 × 10³ × 10⁴
= 1.524 × 10⁷
∴ 15240000 = 1.524 × 10⁷

Question 2.
Write all the facts given in the standard form?
Solution:
A number is said to be in the standard form
when it is written as k × 10ⁿ,
where 1 ≤ k < 10 and ‘n’ is an integer
A number expressed as the product of a number between 1 and 10 and an integral power of 10.
Example: Compare the size of a red blood cell which is 0.000007 m to that of a plant cell which is 0.0000129 m.
Solution:
Size of red blood cell = 0.000007 m
= \(\frac{7}{1000000}\)
= 7 × 10^-6 m
Size of the plant cell = 0.0000129 m

Thus, the size of a red blood cell is half of the plant cell size.