surds and indices Model Questions & Answers, Practice Test for ibps po prelims 2023

Question :11

If $[[{(1/7^2)^{-2}}]^{-1/3}]^{1/4}$ = $7^m$, then find the value of m

Answer: (c)

$[[(1/7^2)^{-2}]^{-1/3}]^{1/4}=7^m$

$⇒[[(7^{-2})^{-2}]^{-1/3}]^{1/4}=7^m$

$⇒[(7^4)^{-1/3}]^{1/4}=7^m$

$⇒(7^{-4/3})^{1/4}=7^m$

$⇒7^{-1/3}=7^m$

$∴m=-1/3$

Question :12

${16 × 32}/{9 × 27 × 81}$ = ?

Answer: (d)

? = ${16 × 32}/{9 × 27 × 81} = {2^4 × 2^5}/{3^2 × 3^3 × 3^4} = {(2)^{4+5}}/{(3)^{2+3+4}} = (2/3)^9$

Question :13

Simplify : $ 13^{1/5}.17^{1/5}$

Answer: (c)

$13^{1/5}.17^{1/5}=(13×17)^{1/5}=221^{1/5}=^5√{221}$

Question :14

On simplification $[{x^{a/{a-b}}/x^{a/{a+b}}÷{x^{b/{b-a}}/x^{b/{b+1}}]]^[a+b]$ reduces to

Answer: (b)

Question :15

$(√9)^3 × (√81)^5 ÷ (27)^2 = (3)^{(?)}$

Answer: (c)

$(√9)^3 × (√81)^5 ÷ (27)^3 = (3)^{(?)}$

$(3)^3 × (9)^5 ÷ (3)^{3 × 2} = (3)^{?}$ or $(3)^3 × (3)^{2 × 5} ÷ (3)^6 = (3)^{?}$

$(3)^{3 + 10 – 6} = (3)^{?}$ or $(3)^7 = (3)^{?}$

? = 7

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