You can Download KSEEB Solutions for Class 8 Maths Chapter 12 Exponents and Powers InText Questions and Answers helps you to revise the complete syllabus.

## KSEEB Solutions for Class 8 Maths Chapter 12 Exponents and Powers InText Questions

Try These (Page 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}

Solution:

(i) Multiplicative inverse of 2^{-4} is 24.

(ii) Multiplicative inverse of 10^{-5} is 105.

(iii) Multiplicative inverse of 7^{-2} is 72.

(iii) Multiplicative inverse of 5^{-3} is 53.

(iv) Multiplicative inverse of 10^{-100} is 10100.

Try These (Page 194)

Question 1.

Expand the following numbers using exponents.

(i) 1025.63

(ii) 1256.249

Solution:

(i) 1025.63

= 1000 + 20 + 5 + \(\frac{6}{10}+\frac{3}{100}\)

= 1 × 10^{3} + 2 × 10 + 5 × 1 + \(\frac{6}{10}+\frac{3}{100}\)

= 1 × 10^{3} + 2 × 10 + 5 × 1 + 6 × 10^{-1} + 3 × 10^{-2}

(ii) 1256.249

= 1000 + 200 + 50 + 6 + \(\frac{2}{10}+\frac{4}{100}+\frac{9}{1000}\)

= 1 × 10^{3} + 2 × 10^{2} + 5 × 10 + 6 × 1 + 2 × 10^{-1} + 4 × 10^{-2} + 9 × 10^{-3}

Try These (Page 195)

Question 1.

Simplify and write in exponential form:

(i) (-2)^{-3} × (-2)^{-4}

(ii) p^{3} × p^{-10}

(iii) 3^{2} × 3^{-5} × 3^{6}

Solution:

(i) (-2)^{-3} × (-2)^{-4}

= (-2)^{3+(-4)}

= (-2)^{-3-4}

= (-2)^{-7}

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

(ii) p^{3} × 10^{-10}

= p^{3+(-10)}

= p^{3-10}

= p^{-7}

= \(\frac{1}{p^{7}}\)

(iii) 3^{2} × 3^{-5} × 3^{6}

= 3^{2-5+6}

= 3^{-3+6}

= 3^{3}

Try These (Page 199)

Question 1.

Write the following numbers in standard form.

(i) 0.000000564

(ii) 0.0000021

(iii) 21600000

(iv) 15240000

Solution:

(i) 0.000000564 = 5.64 × 10^{-7}

(ii) 0.0000021 = 2.1 × 10^{-6}

(iii) 21600000 = 2.16 × 10^{7}

(iv) 15240000 = 1.524 × 10^{7}

Question 2.

Write all the facts given in the standard form.

Solution:

All the facts given in the standard form are as under:

- The distance from the Earth to the Sun is 149,600,000,000 m is 1.496 × 10
^{11}m. - The speed of the light is 300,000,000 m/s = 3.00 × 10
^{8}m/s. - The thickness of the class VII Mathematics book is 20 mm = 2.0 × 10 mm.
- The average diameter of a Red Blood Cell is 0.000007 mm = 7 × 10
^{-6}mm. - 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. - The distance of the Moon from the Earth is 384,467,000 m (approx) = 3.84467 × 10
^{8}m. - The size of a plant cell is 0.00001275 m = 1.275 × 10
^{-5}m. - The average radius of the Sun is 695000 km = 6.95 × 10
^{5}km. - The mass of propellant in a space shuttle solid rocket booster is 503600 kg = 5.036 × 10
^{5}kg. - The thickness of the piece of paper is 0.0016 cm = 1.6 × 10
^{-3}cm. - The diameter of a wire on a computer chip is 0.000003 m = 3 × 10
^{-6}m. - The height of Mount Everest is 8848 m = 8.848 × 10
^{3}m.