NCERT solution class 8 chapter 12 Exponents and Power exercise 12.1

Exercise 12.1

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Introduction - Exponents and Powers - Chapter 12, NCERT Class 8th Maths

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Q 1 - Ex 12.1 -Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 1
Evaluate
(i) 3⁻² (ii) (−4)⁻² (iii)
Sol :
(i)
(ii)
(iii)

Q 2 - Ex 12.1 - Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 2
Simplify and express the result in power notation with positive exponent.
(i) (ii)
(iii) (iv)
(v)
Sol :
(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 =

Q 3 - Ex 12.1 - Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 3
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)
Sol :
(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)

Q 4 - Ex 12.1 - Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 4
Evaluate (i) (ii)
Sol :
(i)

(ii)

Q 5 - Ex 12.1 - Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 5
Find the value of m for which 5^m ÷5⁻³ = 5⁵.
Sol :
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

Q 6 - Ex 12.1 - Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 6
Evaluate (i) (ii)
Sol :
(i)

(ii)

Q 7 - Ex 12.1 - Exponents and Powers - NCERT Maths Class 8th - Chapter 12

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Question 7
Simplify. (i) (ii)
Sol :
(i)

(ii)