simplify and answer in exponential form. a. (-3)^6 × {1/4 } ^2 × (-3)^4 × { 1/3} ^8. b. (2^3)^2× 2^7 × {-1/2}^10. c. [{3/4}^3]^2 × {1/4}^-2× (4)^2 × 1/12. d. (5^-1 - 7^-1 ) ^-2 + (7^-1 - 5^2.
Answers
Step-by-step explanation:
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)-1 ÷ 4-1
(ii) (4-1 + 8-1) ÷ (2/3)-1
Solution:
(i) (2-1 × 5-1)-1 ÷ 4-1
= (1/2 × 1/5)-1 ÷ (4/1)-1
= (1/10)-1 ÷ (1/4)
= 10/1 ÷ 1/4
= (10 ÷ 1/4)
= (10 × 4)
= 40.
(ii) (4-1 + 8-1) ÷ (2/3)-1
= (1/4 + 1/8) ÷ (3/2)
= (2 + 1)/8 ÷ 3/2
= (3/8 ÷ 3/2)
= (3/8 ÷ 2/3)
= 1/4
Answer:
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