NCERT Solution Class 8th Maths Chapter 10 Exponents and Powers Exercise 10.1

(i) 3^-2 (ii) (-4)^-2 (iii) (1/2)^-5  

Solution:

(i) 3^-2 = (1/3)²

= 1/9

(ii) (-4)^-2 = (1/-4)²

= 1/16

(iii) (1/2)^-5 = (2/1)⁵

= 2⁵

= 32

(i) (-4)4 ÷(-4)8   
(ii) (1/23)2  
(iii) -(3)4×(5/3)4
(iv) (3-7÷3-10)×3-5  
(v) 2-3×(-7)-3

Solution:

(i)   

= (-4)⁵/(-4)⁸

= (-4)^5-8

= 1/(-4)³

(ii) (1/2³)²  

= 1²/(2³)²

= 1/2^3×2 = 1/2⁶

(iii) -(3)⁴×(5/3)⁴ 

= (-1)⁴×3⁴×(5⁴/3⁴ )

= 3^(4-4)×5⁴

= 3⁰×5⁴ = 5⁴

(iv) =   (3^-7/3^-10)× 3^-5

= 3^(-7+10)×3^-5

= 3³×3^-5

= 3^(3+-5)

= 3^-2

=1/3²

(v) 2^-3×(-7) ^{– 3}

= (2×-7)^-3

(Because a^m×b^m = (ab)^m)

= 1/(2×-7)³

= 1/(-14)³

(i) (30+4-1)×22
(ii) (2-1×4-1)÷2 – 2
(iii) (1/2)-2+(1/3)-2+(1/4)-2
(iv) (3-1+4-1+5-1)0
(v) {(-2/3)-2}2

Solution:

(i)(3⁰+4^{– 1})×2² = (1+(1/4))×2²

= ((4+1)/4 )×2²

= (5/4)×2²

= (5/2²)×2²

= 5×2^(2-2)

= 5×2⁰

= 5×1 = 5

(ii)(2^-1×4^-1)÷2^-2

= [(1/2)×(1/4)] ÷(1/4)

= (1/2×1/2² )÷ 1/4

= 1/2³÷1/4

= (1/8)×(4)

= 1/2

(iii) (1/2)^-2+(1/3)^-2+(1/4)^-2

= (2^-1)^-2+(3^-1)^-2+(4^-1)^-2

= 2^(-1×-2)+3^(-1×-2)+4^(-1×-2)

= 2²+3²+4²

= 4+9+16

=29

(iv) (3^-1+4^-1+5^-1)⁰

= 1

(v) {(-2/3)^-2}² = (-2/3)^-2×2

= (-2/3)^-4

= (-3/2)⁴

= 81/16

(i) (8-1×53)/2-4
(ii) (5-1×2-2)×6-1 

Solution:

(i) (8^-1×5³)/2^-4

= 2×125 = 250

(ii) (5^-1×2^-2)×6^-1 

= (1/10)×1/6

= 1/60

Solution:

5^m ÷ 5^-3 = 5⁵

5^{(m-(-3) )} = 5⁵

5^m+3 =5⁵

Comparing exponents both sides, we get

m+3 = 5

m = 5-3

m = 2

(i) 

(ii) 

Solution:

(i)

= 3-4

= -1

(ii)

=  512/125

(i)     

(ii) 

Solution:

(i)

(ii) 

 1×1×3125

=  3125