Find the values of each of the following :3^-1 + 4^-1 , (3^-1 + 4^-1 + 5^-1)^0

Question

Find the values of each of the following:

(i) 3-1 + 4-1

(ii) (30 + 4-1) × 22

(iii) (3-1 + 4-1 + 5-1)0

(iv) ((1/3)-1 – (1/4)-1)-1

Answer 1

(i) 3-1 + 4-1

1/3 + 1/4 (we know that a-n = 1/an)

LCM of 3 and 4 is 12

= (1×4 + 1×3)/12

= (4+3)/12

= 7/12

(ii) (30 + 4-1) × 22

(1 + 1/4) × 4 (we know that a-n = 1/an, a0 = 1)

LCM of 1 and 4 is 4

= (1×4 + 1×1)/4 × 4

= (4+1)/4 × 4

= 5/4 × 4

= 5

(iii) (3-1 + 4-1 + 5-1)0

(We know that a0 = 1)

(3-1 + 4-1 + 5-1)0 = 1

(iv) ((1/3)-1 – (1/4)-1)-1

(31 – 41)-1 (we know that 1/a-n = an, a-n = 1/an)

= (3-4)-1

= (-1)-1

= 1/-1

= -1