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?

- 2
^{-4} - 10
^{-5} - 7
^{-2} - 5
^{-3} - 100
^{-100}

Solution:

- The multiplicative inverse of 2
^{-4}is 2^{4}ponents. - The multiplicative inverse of 10
^{-5}is 10^{5} - The multipicative inverse of 7
^{-2}is 7^{2} - The multipicative inverse of 5
^{-3}is 5^{2} - The multipicative inverse of 10
^{-100}is 10^{100}

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?

- (-2)
^{-3}× (-2)^{-4} - p
^{3}× p^{-10} - 3
^{2}× 3^{-5}× 3^{6}

Solution:

1. (-2)^{3} × (-2)^{-4} = (-2)^{(-3)+(-4)} [∵a^{m} × a^{n}]

= (-2)^{-7} or \(\frac{1}{(-2)^{7}}\)

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

3. 3^{2} × 3^{-5} × 3^{6} = 3^{2+(-5)+6} = 3^{8-5} = 3^{3}

Law II: \(\frac{a^{m}}{a^{n}}\) = a^{m-n}

Example: 5^{-1} + 5^{-2} = 5^{-1-(-2)} = 5^{-1+2} = 5^{1} or 5

Law III: (a^{m})^{n} = a^{mn}

Example: (9^{-1})^{-3} = 9^{(-1)×(-3)} = 9^{3}

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: a^{0} = 1

Example:

(i) (-38)^{0} = 1

(ii) (32456)^{0} = 1

Try These (Page 199)

Question 1.

Write the following numbers in standard form?

- 0.000000564
- 0.0000021
- 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 × 10^{3} × 10^{4}

= 1.524 × 10^{7}

∴ 15240000 = 1.524 × 10^{7}

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 × 10^{n},

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.