The value of (√4)-3 is 1/8. This article is about the evaluation of (√4)-3 and the detailed solution for the same is added below:
Evaluate (√4)-3
Solution:
For evaluation of (√4)-3 following exponent formulae are used,
Exponent Formulae a-p = 1/ap
a1/p = p√a
(ap)q = apq
a.a.a..... p times = ap
Let r = (√4)-3
Now, we have to evaluate p using exponents formulae,
r = (√4)-3
r = 1/(√4)3 [(√4)-3 = 1/ (√4)3]
r = 1/[(4)1/2]3 [√4 = 41/2]
r = 1/[(22)1/2]3 [4 = 22]
r = 1/22×(1/2)×3 [(22)1/2]3 = 22×(1/2)×3
r = 1/23
r = 1/8 [23 = 2 × 2 × 2 = 8]
Therefore, the evaluation of (√4)-3 = 1/8
Similar Questions
Question 1: Evaluate:
- 5.5.5.5
- (32)2
- 45/2
Solution:
- 5.5.5.5 = 54 =625
- (32)2 = 32×2 = 34 = 81
- 45/2 = (22)5/2 = 22×(5/2) = 25 = 32
Question 2: Simplify: ( 2-2×72) / 5-1
Solution:
(2-2 × 72) / 5-1 = (51 × 72) / 22
= (5 × 49)/4
= 245/4
Question 3: Find the value of y: (8)y+3 = 4y.26
Solution:
(8)y+3 = 4y.26
[(2)3]y+3 = [(2)2]y.26
23(y+3) = 22×y . 26
23y+9 = 22y+6
Since, bases are same equate powers
3y+ 9 = 2y+6
3y - 2y = 6 - 9
y = -3
Question 4: Find the value of (7292/3)1/2
Solution:
(7292/3)1/2 = {(93)2/3}1/2
= (9)3×(2/3)×(1/2)
= 91
(7292/3)1/2 = 9
Question 5: Find the value of a × b if,
4a = 2a+5; 25b-2 = 5b+4
Solution:
4a = 2a+5
(22)a = 2a+5
22a = 2a+5
Since, bases are same equate the powers
2a = a + 5
a = 5
25b-2 = 5b+4
(52)b-2 = 5b+4
52(b-2) = 5b+4
52b-4 = 5b+4
Since, bases are same equate the powers
2b - 4 = b + 4
2b - b = 4 + 4
b = 8
a × b = 5 × 8 = 40
Question 6: If (-6)p.(36)p-2 = (-6)5, then find (p2 + 4) / (p2 - 4).
Solution:
(-6)p.(36)p-2 = (-6)5
(-6)p.{(-6)2}p-2 = (-6)5
(-6)p.(-6)2(p-2) = (-6)5
(-6)p.(-6)2p-4 = (-6)5
(-6)p+2p-4 = (-6)5
(-6)3p-4 = (-6)5
Since, bases are same equate the powers,
3p - 4 = 5
3p = 9
p = 3
(p2 + 4) / (p2 - 4) = (32 + 4) / (32 - 4)
= (9 + 4) / (9 - 4)
(p2 + 4) / (p2 - 4) = 13 / 5
Question 7: Find the multiplicative inverse of [(14)-1]2÷(84)-2.
Solution:
[(14)-1]2 ÷ (84)-2 = (14)-2 ÷ (1/842)
= (1/142) × 842
= 842 / 142
= (84 × 84)/(14 × 14)
= 6 × 6
[(14)-1]2 ÷ (84)-2 = 36