Question

Evaluate (-¾)-⁷ × (-⁴/9)-⁵​

Answer 1

Answer:

1. Evaluate the exponent:

(i) 5-3

(ii) (1/3)-4

(iii) (5/2)-3

(iv) (-2)-5

(v) (-3/4)-4

We have:

(i) 5-3 = 1/53 = 1/125

(ii) (1/3)-4 = (3/1)4 = 34 = 81

(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

3. Evaluate: (-1/4)-3 × (-1/4)-2

Solution:

(-1/4)-3 × (-1/4)-2

= (4/-1)3 × (4/-1)2

= (-4)3 × (-4)2

= (-4)(3 + 2)

= (-4)5

= -45

= -1024.

4. Evaluate: {[(-3)/2]2}-3

Solution:

{[(-3)/2]2}-3

= (-3/2)2 × (-3)

= (-3/2)-6

= (2/-3)6

= (-2/3)6

= (-2)6/36

= 26/36

= 64/729

5. Simplify:

(i) (2-1 × 5-1)