Exercise 12.1 - Chapter 12 Exponents & Powers class 8 ncert solutions Maths - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 1:

Evaluate

(i) 3⁻² (ii) (−4)⁻² (iii) 

Answer:

(i) 

(ii) 

(iii) 

Question 2:

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} (am ÷ an = am ⁻ n)

= (− 4)⁻³

(ii) 

(iii) 

(iv) (3^{− 7} ÷ 3⁻¹⁰) × 3⁻⁵ = (3^{−7 − (−10)}) × 3⁻⁵ (am ÷ an = am ⁻ n)

= 3³ × 3⁻⁵

= 3^{3 + (− 5)} (am × an = am ⁺ n)

= 3⁻²

(v) 2⁻³ × (−7)⁻³ = 

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) 

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 (am × an = am ⁺ n)

= 2⁻³ ÷ 2⁻²

= 2^{−3 − (−2)} (am ÷ an = am ⁻ n)

= 2^{−3 + 2} = 2 ⁻¹

(iii) 

(iv) (3⁻¹ + 4⁻¹ + 5⁻¹)⁰

= 1 (a⁰ = 1)

(v) 

Question 4:

Evaluate (i)   (ii) 

Answer:

(i) 

(ii) 

Question 5:

Find the value of m for which 5m ÷5⁻³ = 5⁵.

Answer:

5m ÷ 5⁻³ = 5⁵

5m ^{− (− 3)} = 5⁵ (am ÷ an = am ⁻ n)

5m ^{+ 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

Question 6:

Evaluate (i)   (ii) 

Answer:

(i) 

(ii) 

Question 7:

Simplify. (i)   (ii) 

Answer:

(i) 

(ii)