Exercise 12.1

Question 1.


(i) Exponents and Powers/image001.png(ii) Exponents and Powers/image002.png (iii) Exponents and Powers/image003.png

Solution :

(i) Exponents and Powers/image001.png= 1/3²

Exponents and Powers/image005.png

= 1/9

(ii) Exponents and Powers/image007.png

Exponents and Powers/image005.png

= 1/16

(iii) Exponents and Powers/image003.pngExponents and Powers/image009.png

Exponents and Powers/image005.png

Exponents and Powers/image010.png= 32

Question 2.

Simplify and express the result in power notation with positive exponent:

(i) Exponents and Powers/image011.png

(ii) Exponents and Powers/image012.png

(iii) Exponents and Powers/image013.png

(iv) Exponents and Powers/image014.png

(v) Exponents and Powers/image014.png

Solution :

(i)Exponents and Powers/image016.pngExponents and Powers/image017.pngExponents and Powers/image018.png

Exponents and Powers/image019.pngExponents and Powers/image005.png

(ii) Exponents and Powers/image020.png

Exponents and Powers/image021.png

Exponents and Powers/image022.pngExponents and Powers/image023.png

(iii) Exponents and Powers/image024.pngExponents and Powers/image021.png

Exponents and Powers/image025.png

Exponents and Powers/image026.png

Exponents and Powers/image027.pngExponents and Powers/image018.png

Exponents and Powers/image028.pngExponents and Powers/image029.png

(iv) Exponents and Powers/image030.pngExponents and Powers/image018.png

Exponents and Powers/image031.pngExponents and Powers/image032.pngExponents and Powers/image033.pngExponents and Powers/image034.png

Exponents and Powers/image035.pngExponents and Powers/image005.png

Exponents and Powers/image036.png

Question 3.

Find the value of:

Exponents and Powers/image039.png

Solution :

Exponents and Powers/image044.png
Exponents and Powers/image048.png
Exponents and Powers/image058.png

Question 4.


Exponents and Powers/image063.png

Solution :

Exponents and Powers/image065.png

= 1/10 × 1/6 = 1/60

Question 5.
Find the value of m for which Exponents and Powers/image071.png

Solution :

Exponents and Powers/image071.png
Exponents and Powers/image073.png
Exponents and Powers/image074.png
Exponents and Powers/image018.png
Exponents and Powers/image073.png
Exponents and Powers/image074.png

Comparing exponents both sides, we get

Exponents and Powers/image073.png  m+3 = 5

Exponents and Powers/image073.png  m = 5 – 3

  Exponents and Powers/image073.png m = 2

Question 6.

Exponents and Powers/image079.png

Question 7.

Exponents and Powers/image090.png
Exponents and Powers/image026.png

NCERT Solutions for Class 8 Maths Exercise 12.2

Question 1.

Express the following numbers in standard form:

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000

Solution :

(i) 0.0000000000085

= 0.0000000000085 Exponents and Powers/image001.pngExponents and Powers/image002.png

Exponents and Powers/image003.png

(ii) 0.00000000000942

= 0.00000000000942 Exponents and Powers/image001.pngExponents and Powers/image002.png

=Exponents and Powers/image004.png

(iii) 6020000000000000

= 6020000000000000 Exponents and Powers/image001.pngExponents and Powers/image005.png

Exponents and Powers/image006.png

(iv) 0.00000000837

= 0.00000000837 Exponents and Powers/image001.pngExponents and Powers/image007.png

Exponents and Powers/image008.png

(v) 31860000000 = 31860000000 Exponents and Powers/image001.pngExponents and Powers/image009.pngExponents and Powers/image010.png

Question 2.

Express the following numbers in usual form :

Exponents and Powers/image011.png

Solution :

Exponents and Powers/image017.png

Question 3.

Express the number appearing in the following statements in standard form :

(i)1 micron is equal to 1/ 1000000 m.

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

(iii) Size of a bacteria is 0.0000005 m.

(iv) Size of a plant cell is

0.00001275 m.

(v) Thickness if a thick paper is 0.07 mm.

Solution :

(i) 1 micron

Exponents and Powers/image021.pngm

(ii)Charge of an electron is

0.00000000000000000016 coulombs.

= 0.00000000000000000016 Exponents and Powers/image001.pngExponents and Powers/image022.png

Exponents and Powers/image023.pngcoulomb

(iii) Size of bacteria = 0.0000005

Exponents and Powers/image024.pngExponents and Powers/image025.pngm

(iv) Size of a plant cell is 0.00001275 m

= 0.00001275 Exponents and Powers/image001.pngExponents and Powers/image026.pngExponents and Powers/image027.pngm

(v) Thickness of a thick paper = 0.07 mm

= 7/100mm = Exponents and Powers/image029.pngmm

Question 4.

In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?

Solution :

Thickness of one book = 20 mm

Thickness of 5 books = 20 × 5 = 100 mm

Thickness of one paper = 0.016 mm

Thickness of 5 papers = 0.016 × 5

= 0.08 mm

Total thickness of a stack = 100 + 0.08

=100.08 mm

= 100.08 Exponents and Powers/image001.pngExponents and Powers/image030.png

Exponents and Powers/image031.pngmm

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