Surds & Indices Problems To Prepare For IBPS Exam

Dear Reader,
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
Answer : b) 1331

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
Answer : a) 1000
Solution :
Given expression is (10000)⁶ / 10²¹
= [(10⁴)]⁶ / 10²¹.
By using the formula, (a^m)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
Answer : b) 5
Solution :
Given expression is [(3125)^0.11] x [(3125)^0.09]
By using the formula, (a^m)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.