2to the power n-5×6to the power 2n-4=9to the power n×8devided by 12to the power 4×2
Answers
i am giving you example just
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)-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
6. Simplify: (1/2)-2 + (1/3)-2 + (1/4)-2
Solution:
(1/2)-2 + (1/3)-2 + (1/4)-2
= (2/1)2 + (3/1)2 + (4/1)2
= (22 + 32 + 42)
= (4 + 9 + 16)
= 29.
7. By what number should (1/2)-1 be multiplied so that the product is (-5/4)-1?
Solution:
Let the required number be x. Then,
x × (1/2)-1 = (-5/4)-1
⇒ x × (2/1) = (4/-5)
⇒ 2x = -4/5
⇒ x = (1/2 × -4/5) = -2/5
Hence, the required number is -2/5.
8. By what number should (-3/2)-3 be divided so that the quotient is (9/4)-2?
Solution:
Let the required number be x. Then,
(-3/2)-3/x = (9/4)-2
⇒ (-2/3)3 = (4/9)2 × x
⇒ (-2)3/33 = 42/92 × x
⇒ -8/27 = 16/81 × x
⇒ x = {-8/27 × 81/16}
⇒ x = -3/2
Hence, the required number is -3/2
9. If a = (2/5)2 ÷ (9/5)0 find the value of a-3.
Solution:
a-3 = [(2/5)2 ÷ (9/5)0]-3
= [(2/5)2 ÷ 1]-3
= [(2/5)2]-3
= (2/5)-6
= (5/2)6
10. Find the value of n, when 3-7 ×32n + 3 = 311 ÷ 35
Solution:
32n + 3 = 311 ÷ 35/3-7
⇒ 32n + 3 = 311 - 5/3-7
⇒ 32n + 3 = 36/3-7
⇒ 32n + 3 = 36 - (-7)
⇒ 32n + 3 = 36 + 7
⇒ 32n + 3 = 313
Since the bases are same and equating the powers, we get 2n + 3 = 13
2n = 13 – 3
2n = 10
n = 10/2
Therefore, n = 5
11. Find the value of n, when (5/3)2n + 1 (5/3)5 = (5/3)n + 2
Solution:
(5/3)2n + 1 + 5 = (5/3)n + 2
= (5/3)2n + 6 = (5/3)n + 2
Since the bases are same and equating the powers, we get 2n + 6 = n + 2
2n – n = 2 – 6
=> n = -4
12. Find the value of n, when 3n = 243
Solution:
3n = 35
Since, the bases are same, so omitting the bases, and equating the powers we get, n = 5.
13. Find the value of n, when 271/n = 3
Solution:
(27) = 3n
⇒ (3)3 = 3n
Since, the bases are same and equating the powers, we get
⇒ n = 3
14. Find the value of n, when 3432/n = 49
Solution:
[(7)3]2/n = (7)2
⇒ (7)6/n = (7)2
⇒ 6/n = 2
Since, the bases are same and equating the powers, we get n = 6/2 = 3.