Find n if (-5/7)⁴ × (-5/7)¹² = {(-5/7)³}ⁿ × (-5/7)¹.
Answers
Answer:
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
Step-by-step explanation:
(-5/7)⁴×(-5/7)¹²
=(-5/7)⁴+¹²
=(-5/7)^16
and {(-5/7)³}^n
=(-5/7)^3n
and
(-5/7)^3n × (-5/7)^1
=(-5/7)^3n+1
so (-5/7)^16=(-5/7)^3n+1. (-5/7 and -5/7 cancelled)
=>16=3n+1
=>16-1=3n
=>15=3n
=>n=15/3=5