Surds and Indices | Aptitude Questions with Answers

Directions: Solve the following questions applying the various indices and surds formulas.

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Example 1: Simplify (27/1331)^2/3 x (121/9)^1/2

Sol:

⇒ (3/11)² x (11/3)
⇒ 9/121 x 11/3 = 3/11

Example 2: Simplify 7^-3 x 343^5/3 x (2401)^-3/4

Sol: 7^-3 x (7³)^5/3 x (7⁴)^-3/4
⇒1/7³ x 7⁵ x 7^-3
⇒1/7³ x 7⁵ x 1/7³ = 1/7

Example 3: Simplify Indices and Surds Solved

Sol:

⇒

= 11^n+1-n x 31/13 = 341/13

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Example 4: Simplify 7^{3x –2} = 2401 find value of x

Sol: 7^{3x –2} = 7⁴
So 3x – 2 = 4
⇒ 3x = 6
x = 2

Example 5: √(5/7)^6x-4 = 2401/875 Find value of x

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Sol: (5/7)^3x-4 = 7⁴/(7 x 5³) = (7/5)³
(5/7)^3x-4 = (5/7)^-3
3x – 2 = -3
3x = - 1
x = - 1/3

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