## Surds & Indices Problems To Prepare For IBPS Exam

Below are four problems based on surds and indices.

Question 1

The value of [(11)148 / (11)145] is:

a) 14641 b) 1331 c) 11^293 d) none of these

Solution :

Using the formula, [(a)m /(a)n] = a(m-n).
Given expression is [(11)148 / (11)145]
Here, a = 11, m = 148 and n = 145,
= [11(148-145)]
= [(11)3]
= 1331

Question 2

The value of (2.7 x 104) / (9 x 10-3) is:

a) .3 x 106 b) 3 x 10-6 c) .03 x 106 d) 3 x 106

Answer : d) 3 x 106

Solution :

Given expression is (2.7 x 104) / (9 x 10-3)
= (27 x 103) / (9 x 10-3)
= (3 x 103) / (10-3)
= [3 x 10(3-(-3))]
= [3 x 10(3+3)]
= 3 x 106

Question 3

Find the value of (10000)6 / 1021.

a) 1000 b) 10-27 c) 100 d) none of these

Solution :

Given expression is (10000)6 / 1021
= [(104)]6 / 1021.
By using the formula, (am)n = a(mn), we have
= (10)24 / 1021.
= 10(24-21)
= 103
= 1000

Question 4

Find the value of [(3125)0.11] x [(3125)0.09].

a) 25 b) 5 c) 125 d) none of these

Solution :

Given expression is [(3125)0.11] x [(3125)0.09]
By using the formula, (am)x(an) = a(m+n).
Here, a = 3125, m = 0.11 and n = 0.09, then we have,
= [3125(0.11+0.09)]
= 3125(0.20)
= 3125(20/100)
= 3125(1/5)
= (55)(1/5) (since 55 = 3125)
= (5)(5 x 1/5)
= 5.

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