# NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers| PDF Download

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**Exercise 12.1**

1. Evaluate:

(i) 3

^{-2}

(ii) (-4)

^{-2}

(iii) (1/2)

^{-5}Â

**Answer**

(i) 3

^{-2}

= 1/3

^{2}Â [Â âˆµÂ a

^{-m}Â = 1/a

^{m}Â ]

= 1/9

(ii) (-4)

^{-2}

= 1/(-4)

^{2}[âˆµ a-mÂ = 1/amÂ ]

= 1/16

(iii)Â (1/2)

^{-5}

= (2/1)

^{5}Â [Â âˆµÂ a-mÂ = 1/amÂ ]

Â = (2)

^{5}Â = 32

**2.Â Simplify and express the result in power notation with positive exponent:**

(i) ( -4)

^{5}Â Ã·Â (-4)

^{8}Â

(ii) (1/2

^{3})

^{2}Â

(iii) (-3)

^{4}Â Ã— (5/3)

^{4}Â

(iv) (3

^{-5}Â Ã· 3

^{-10})Â Ã—Â 3

^{-5}

(v) 2

^{-3}Â Ã—Â (-7)

^{-3}Â

**Answer**

(i)Â ( -4)

^{5}Â Ã·Â (-4)

^{8}

= (-4)

^{5-8}[Â âˆµÂ a

^{m}Ã·Â a

^{n}Â = a

^{m-n}]

= (-4)

^{-3}

= 1/(-4)

^{3}[âˆµ a

^{-m}Â = 1/a

^{m}Â ]

(ii)Â (1/2

^{3}Â )

^{2}

= 1

^{2}/(2

^{3})

^{2}Â [âˆµÂ (a/b)

^{m}Â = a

^{m}/a

^{n}]

= 1/2

^{3}Ã—

^{2}

= 1/2

^{6}Â [(a

^{m})

^{n}Â = a

^{m}Ã—

^{n}]

(iii)Â (-3)

^{4}Â Ã— (5/3)

^{4}

= (-3)

^{4}Â Ã— 5

^{4}/3

^{4}[âˆµ (a/b)

^{m}Â = a

^{m}/a

^{n}]

= {(-1)

^{4}Â Ã— 3

^{4}}Â Ã— 5

^{4}/3

^{4Â }[Â âˆµÂ (ab)

^{m}Â = a

^{m}b

^{m}]

= 3

^{4-4}Â Ã— 5

^{4}Â [Â âˆµÂ a

^{m}Â

**Ã·Â**a

^{n}Â = a

^{m-n}]

= 3

^{0}Â Ã— 5

^{4}

= 5

^{4}Â [a

^{0}Â = 1]

(iv) (3

^{-7}Â

**Ã·Â**3

^{-10})Â Ã— 3

^{-5}

= 3

^{-7-(-10)}Â Ã— 3

^{-5}Â [âˆµÂ a

^{m}Â

**Ã·Â**a

^{n}Â = a

^{m-n}]

= 3

^{-7+10}Â Ã— 3

^{-5}

= 3

^{3}Â Ã— 3

^{-5}Â = 3

^{3+(-5)}Â [âˆµÂ a

^{m}Â Ã— a

^{n}Â = a

^{m+n}]

=3

^{-2}

= 1/3

^{2}Â [a

^{-m}Â = 1/a

^{m}]

(v)Â 2

^{-3}Â Ã— (-7)

^{-3}

= 1/2

^{3}Â Ã—1/(-7)

^{3}[âˆµÂ a

^{-m}Â = 1/a

^{m}]

= 1/{2Â Ã— (-7)}

^{3}

= 1/(-14)

^{3}Â [âˆµÂ (ab)

^{m}Â = a

^{m}b

^{m}]

**3.Â Find the value of:**

(i) (3

^{0}Â + 4

^{-1})Â Ã— 2

^{2}

(ii) (2

^{-1}Â Ã— 4

^{-1})Â Ã·Â 2

^{-2}Â

(iii) (1/2)

^{-2}Â + (1/3)

^{-2}Â + (1/4)

^{-2}Â

(iv) (3

^{-1}Â + 4

^{-1}Â + 5

^{-1})

^{0}Â

(v) {(-2/3)

^{-2}}

^{2}Â

**AnswerÂ**

(i) ( 3

^{0}Â + 4

^{-1})Â Ã— 2

^{2}

= (1 + 1/4)Â Ã— 2

^{2}[âˆµ a

^{-m}Â = 1/a

^{m}]

= {(4 + 1)/4}Â Ã— 2

^{2}

= 5/4Â Ã— 2

^{2}

= 5/2

^{2}Â Ã— 2

^{2}

= 5Â Ã— 2

^{2-2}[âˆµÂ a

^{m}Â Ã·Â a

^{n}Â = a

^{m-n}]

= 5Â Ã— 2

^{0}

= 5Â Ã— 1

= 5 [âˆµÂ a

^{0}Â = 1]

(ii)Â ( 2

^{-1}Â Ã— 4

^{-1})Â

**Ã·Â**2

^{-2}Â =[âˆµ a

^{-m}Â = 1/a

^{m}]

=Â [âˆµ a

^{m}Â Ã—a

^{n}Â = a

^{m+n}]

=[âˆµ a

^{m}Â Ã·Â a

^{n}Â = a

^{m-n}]

= 1/2 [âˆµ a

^{-m}Â = 1/a

^{m}]

(iii) (1/2)

^{-2}Â + (1/3)

^{-3}Â + (1/4)

^{-2}

= (2

^{-1})

^{-2}Â + (3

^{-1})

^{-2}Â + (4

^{-1})

^{-2}Â [âˆµ a

^{-m}Â = 1/a

^{m}]

= 2

^{-1Ã—(-2)}Â + (3)

^{-1Ã—(-2)}Â + (4)

^{-1Ã—(-2)}Â [âˆµÂ (a

^{m})

^{n}Â = a

^{mÃ—n}]

= 2

^{2}Â + 3

^{2}Â + 4

^{2}

= 4 + 9 + 16

= 29

(iv)Â (3 + 4 + 5)

^{0}

= (1/3 + 1/4 + 1/5)

^{0}[âˆµ a

^{-m}Â = 1/a

^{m}]

= {(20 + 15 + 12)/60}

^{0}

= (47/60)

^{0}

= 1 [âˆµ a

^{0}Â = 1]

(v) [âˆµ (a

^{m})

^{n}Â = a

^{mÃ—n}]

=Â [âˆµ a

^{-m}Â = 1/a

^{m}]

= 81/16

4. Evaluate:

(i) (8

^{-1}Â Ã— 5

^{3})/2

^{-4}Â

(ii) ( 5

^{-1}Â Ã— 2

^{-1})Â Ã— 6

^{-1}Â

**Answer**

(i) (8

^{-1}Â Ã— 5

^{3})/2

^{-4}

= (8

^{-1}Â Ã— 5

^{3})/2

^{-4}

= {(2

^{3})

^{-1}Â Ã— 5

^{3}}/2

^{-4}

= (2

^{-3}Â Ã— 5

^{3})/2

^{-4}Â [âˆµ (a

^{m})

^{n}Â = a

^{mÃ—n}]

= 2

^{-3(-4)}Â Ã— 5

^{3}

= 2

^{-3+4}Â Ã— 5

^{3}[âˆµ a

^{m}Â Ã·Â a

^{n}Â = a

^{m-n}]

= 2Ã—125

= 250

(ii)( 5

^{-1}Â Ã—Â 2

^{-1}) 6

^{-1}

= (1/5Â Ã— 1/2)Â Ã— 1/6 [âˆµ a

^{-m}Â = 1/a

^{m}]

= 1/10Â Ã— 1/6 = 1/60

**5.Â Find the value of mÂ for which 5**

^{m}Â Ã·Â 5

^{-3}Â = 5

^{5}Â

**Answer**

5

^{m}Â Ã·Â 5

^{-3}Â = 5

^{5}

= 5

^{m-(-3)}Â = 5

^{5}Â [âˆµ a

^{m}Â Ã·Â a

^{n}Â = a

^{m-n}]

â‡’Â 5

^{m+3}Â = 5

^{5}

Comparing exponents both sides, we get

â‡’Â m + 3 = 5

â‡’Â m = 5 - 3

â‡’Â m = 2

6. Evaluate:

(i)Â

(ii)Â

**Answer**

(i)Â

= [âˆµ a

^{-m}Â = 1/a

^{m}]

={3 -4} = -1

(ii)Â

=Â

=Â [âˆµ a

^{m}Â Ã·Â a

^{n}Â = a

^{m-n}]

=Â [âˆµ a

^{-m}Â = 1/a

^{m}]

= 512/125

7. Simplify:

(i)Â

(ii)Â

**Answer**

(i)

=Â

=Â Â

=Â

(ii)

=

=

=Â

=Â

=Â

= 1Ã—1Ã—3125 [âˆµ a

^{0}Â = 1]

= 3125

Page No. 200

**Exercise 12.2**

1. Express the following numbers in standard form:

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000

**Answer**

(i)Â 0.0000000000085

= (0.0000000000085Ã—10

^{12})/10

^{12}

= 8.5Â Ã—Â 10

^{-12}

(ii)Â 0.00000000000942

= (0.00000000000942Ã—10

^{12})/10

^{12}

= 9.42Â Ã—10

^{-12}

(iii)Â 6020000000000000

= (6020000000000000Ã—10

^{15)}/10

^{15}

= 6.02Â Ã—Â 10

^{15}

(iv)Â 0.00000000837

= (0.00000000837Ã—10

^{9})/10

^{9}

= 8.37Â Ã—Â 10

^{-9}

(v)Â 31860000000

= 31860000000Â Ã— 10

^{10}/10

^{10}Â = 3.186Â Ã—10

^{10}

2. Express the following numbers in usual form:

(i) 3.02Â Ã— 10

^{-6}Â

(ii) 4.5Â Ã— 10

^{4}Â

(iii) 3Â Ã— 10

^{-8}Â

(iv) 1.0001Â Ã— 10

^{9}Â

(v) 5.8Â Ã— 10

^{12}Â

(vi) 3.61492Â Ã— 10

^{6}Â

**Answer**

(i) 3.02Â Ã— 10

^{-6}

= 3.02/10

^{6}

= 0.00000302

(ii) 4.5Â Ã— 10

^{4}

=Â 4.5Â Ã—Â 10000

= 45000

(iii) 3Â Ã— 10

^{-8}

= 3/10

^{8}

= 0.00000003

(iv)Â 1.0001Â Ã— 10

^{9}

= 1000100000

(v) 5.8Â Ã— 10

^{12}

= 5.8Â Ã—Â 1000000000000

= 5800000000000

(vi)Â 3.61492Â Ã— 10

^{6}

= 3.61492Â Ã—Â 1000000

= 3614920

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.

**Answer**

(i)Â 1 micron

= 1/1000000

= 1/10

^{6}Â = 1Â Ã—Â 10

^{-6}Â m

(ii)Charge of an electron is

0.00000000000000000016 coulombs.

= (0.00000000000000000016Ã—10

^{19})/10

^{19}

= 1.6Â Ã— 10

^{-19}Â coulomb

(iii)Â Size of bacteria = 0.0000005

5/10000000

=5Ã—10

^{7}

=5Ã—10

^{âˆ’7}

(iv)Â Size of a plant cell is 0.00001275 m

= (0.00001275Â Ã—Â 10

^{5})/10

^{5}

= 1.275Â Ã—Â 10

^{-5}Â m

(v)Â Thickness of a thick paper = 0.07 mm

= 7/100 mm = 7/10

^{2}Â = 7Â Ã—Â 10

^{-2}Â mm

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?

**Answer**

Thickness of one book = 20 mm

Thickness of 5 books = 20Â Ã—Â 5 = 100 mm

Thickness of one paper = 0.016 mm

Thickness of 5 papers = 0.016Â Ã—Â 5 = 0.08 mm

Total thickness of a stack = 100 + 0.08

=100.08 mm

= 100.08Â Ã— 10

^{2}/10

^{2}

= 1.0008Â Ã—Â 10

^{2}Â mm

**Go Back ToÂ NCERT Solutions for Class 8 Maths**

## NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

Chapter 12 Exponents and Powers will be useful in obtaining good marks in the examinations. 8 Ã— 8 can be written as 8

^{2}. In 8^{2}, the number 8 is called the base and 2 is called the exponent or the power.â€¢ Laws of exponents:

(i) x

^{m}Ã— x^{n}= x^{m+n}(ii) x

^{m}Ã· x^{n}= x^{m-n}(iii) (x

^{m})^{n}= x^{mÃ—n}(iv) x

^{m}Ã— y^{m}= (xy)^{m}(v) x

^{m}/y^{m}= (x/y)^{m}â€¢ The value of any number raised to 0 is 1, i.e. a

^{0}= 1.â€¢ A number is said to be in the standard form, if it is expressed as the product of a number between 1 and 10 and the integral power of 10.

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### NCERT Solutions for Class 8 Maths Chapters:

**FAQ onÂ ChapterÂ**

**12 Exponents and Powers**

#### How many exercises in Chapter 12 Exponents and Powers Class 8 Maths?

There are total two exercises in the Chapter 12 Class 8 Maths textbook through which a student can learn variety of concepts and formulas that is going to help them in higher classes also. You can clear your doubts if you have any with the help of these NCERT Solutions.

#### If x^{11} = y^{0} and x=2y, then y is equal to?

x

^{11}= y^{0}=> x^{11}= 1 => x = 1. Given, x = 2y hence, y = x/2 =1/2.#### What is the value of 6^{3}?

6

^{3}= 6 Ã— 6 Ã— 6

= 36 Ã— 6

= 216.

#### Write 34500000 in standard form.

34500000 = 345 Ã— 100000

= 3.45 Ã— 100 Ã— 100000

= 3.45 Ã— 10

^{2}Ã— 10^{5}= 3.45 Ã— 10^{2}+5= 3.45 Ã— 10

^{7}Thus, 34500000 = 3.45 Ã— 10

^{7}.