# Aptitude - Surds and Indices

Exercise : Surds and Indices - General Questions
6.
(256)0.16 x (256)0.09 = ?
4
16
64
256.25
Explanation:

(256)0.16 x (256)0.09 = (256)(0.16 + 0.09)

= (256)0.25

= (256)(25/100)

= (256)(1/4)

= (44)(1/4)

= 44(1/4)

= 41

= 4

7.
The value of [(10)150 ÷ (10)146]
1000
10000
100000
106
Explanation:

 (10)150 ÷ (10)146 = 10150 10146

= 10150 - 146

= 104

= 10000.

8.
 1 + 1 + 1 = ? 1 + x(b - a) + x(c - a) 1 + x(a - b) + x(c - b) 1 + x(b - c) + x(a - c)
0
1
xa - b - c
None of these
Explanation:

Given Exp. =
1  +  1  +  1
 1 + xb + xc xa xa
 1 + xa + xc xb xb
 1 + xb + xa xc xc

 = xa + xb + xc (xa + xb + xc) (xa + xb + xc) (xa + xb + xc)

 = (xa + xb + xc) (xa + xb + xc)

= 1.

9.
(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?
8.5
13
16
17.5
None of these
Explanation:

Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.

 Then, (52)7.5 x (5)2.5 = 5x (53)1.5

 5(2 x 7.5) x 52.5 = 5x 5(3 x 1.5)

 515 x 52.5 = 5x 54.5

5x = 5(15 + 2.5 - 4.5)

5x = 513

x = 13.

10.
(0.04)-1.5 = ?
25
125
250
625
Explanation:

 (0.04)-1.5 = 4 -1.5 100

 = 1 -(3/2) 25

= (25)(3/2)

= (52)(3/2)

= (5)2 x (3/2)

= 53

= 125.