Question

evaluate the following a) (24/5)power -4 ÷ (12/15)power6 ×(6/4)power 5, (b) (6power2÷2power2 ÷ 3power2)power-2​

Answer 1

(iii) (5/2)-3 = (2/5)3 = 23/53 = 8/125

(iv) (-2)-5 = 1/(-2)-5 = 1/-25 = 1/-32 = -1/32

(v) (-3/4)-4 = (4/-3)4 = (-4/3)4 = (-4)4/34 = 44/34 = 256/81

2. Evaluate: (-2/7)-4 × (-5/7)2

Solution:

(-2/7)-4 × (-5/7)2

= (7/-2)4 × (-5/7)2

= (-7/2)4 × (-5/7)2 [Since, (7/-2) = (-7/2)]

= (-7)4/24 × (-5)2/72

= {74 × (-5)2}/{24 × 72 } [Since, (-7)4 = 74]

= {72 × (-5)2 }/24

= [49 × (-5) × (-5)]/16

= 1225/16