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

Below are the step by step solutions of questions covered in chapter 12 of class 8 Maths.

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

The following topics covered in this chapter:

Exercise 12.1 : Solutions of Questions on Page Number : 197

Q1 : Evaluate
(i) 3 ^{– 2} (ii) ( – 4) ^{– 2} (iii)
Answer :
(i)
(ii)
(iii)

Q2 :Simplify and express the result in power notation with positive exponent.
(i) (ii)
(iii) (iv)
(v)
Answer :
(i) ( – 4)⁵ ÷( – 4)⁸ = ( – 4)^{5 – 8} (a^m ÷ aⁿ = a^{m – n})
= ( – 4) ^{– 3}


(ii)
(iii)

(iv) (3 ^{– 7} ÷ 3 ^{– 10}) × 3 ^{– 5} = (3 ^{– 7 – ( – 10)}) × 3 ^{– 5} (a^m ÷ aⁿ = a^{m – n})
= 3³ × 3 ^{– 5}
= 3^{3 + ( – 5)} (a^m × aⁿ = a^{m + n})
= 3 ^{– 2}


(v) 2 ^{– 3} × ( – 7) ^{– 3} =

Q3 : Find the value of.
(i) (3⁰ + 4 ^{– 1}) × 2²
(ii) (2 ^{– 1} × 4 ^{– 1}) ÷2 ^{– 2}
(iii) (iv) (3 ^{– 1} + 4 ^{– 1} + 5 ^{– 1})⁰
(v)
Answer :
(i)
(ii) (2 ^{– 1} × 4 ^{– 1}) ÷ 2 ^{– 2} = [2 ^{– 1} × {(2)²} ^{– 1}] ÷ 2 ^{– 2}
= (2 ^{– 1} × 2 ^{– 2}) ÷ 2 ^{– 2}= 2 ^{– 1+ ( – 2)} ÷ 2 ^{– 2} (a^m × aⁿ = a^{m+ n})
= 2 ^{– 3} ÷ 2 ^{– 2}
= 2 ^{– 3 – ( – 2)} (a^m ÷ aⁿ = a^{m – n})
= 2 ^{– 3 + 2} = 2 ^{– 1}

(iii)

(iv) (3 ^{– 1} + 4 ^{– 1} + 5 ^{– 1})⁰
= 1 (a⁰ = 1)
(v)

Q4 : Evaluate (i) (ii)
Answer :
(i)

(ii)

Q5 : Find the value of m for which 5^m ÷5^-3 = 5⁵.

Answer :
5^m ÷ 5^-3 = 5⁵
5^{m – (- 3)} = 5⁵ (a^m ÷ aⁿ = a^{m– n})
5^{m+ 3} = 5⁵
Since the powers have same bases on both sides, their respective exponents must be equal.
m + 3 = 5
m = 5 – 3
m = 2

Q6 : Evaluate (i) (ii)
Answer :
(i)

(ii)

Q7 : Simplify. (i) (ii)
Answer :
(i)

(ii)

Exercise 12.2 : Solutions of Questions on Page Number : 200

Q1 :Express the following numbers in standard form.
(i) 0.0000000000085 (ii) 0.00000000000942
(iii) 6020000000000000 (iv) 0.00000000837
(v) 31860000000

Answer :
(i) 0.0000000000085 = 8.5 x 10^-12
(ii) 0.00000000000942 = 9.42 x 10^-12
(iii) 6020000000000000 = 6.02 x 10¹⁵
(iv) 0.00000000837 = 8.37 x 10^-9
(v) 31860000000 = 3.186 x 10¹⁰

Q2 :Express the following numbers in usual form.
(i) 3.02 x 10^-6 (ii) 4.5 x 10⁴
(iii) 3 x 10^-8 (iv) 1.0001 x 10⁹
(v) 5.8 x 10¹² (vi) 3.61492 x 10⁶

Answer :
(i) 3.02 x 10^-6 = 0.00000302
(ii) 4.5 x 10⁴ = 45000
(iii) 3 x 10^-8 = 0.00000003
(iv) 1.0001 x 10⁹ = 1000100000
(v) 5.8 x 10¹² = 5800000000000
(vi) 3.61492 x 10⁶ = 3614920

Q3 :Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to 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 of a thick paper is 0.07 mm

Answer :
(i) = 1 × 10 ^{– 6}
(ii) 0.000, 000, 000, 000, 000, 000, 16 = 1.6 × 10 ^{– 19}
(iii) 0.0000005 = 5 × 10 ^{– 7}
(iv) 0.00001275 = 1.275 × 10 ^{– 5}
(v) 0.07 = 7 × 10 ^{– 2}

Q4 :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 each book = 20 mm
Hence, thickness of 5 books = (5 x 20) mm = 100 mm
Thickness of each paper sheet = 0.016 mm
Hence, thickness of 5 paper sheets = (5 x 0.016) mm = 0.080 mm
Total thickness of the stack = Thickness of 5 books + Thickness of 5 paper sheets
= (100 + 0.080) mm
= 100.08 mm
= 1.0008 x 10² mm