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Surds and Indices: Solved Examples

Go through the given solved examples based on surds and indices to understand the concept better.
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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:[image] Indices and Surds Solved" class="circular2" src="https://mba.hitbullseye.com/sites/default/files/surdsolved1.svg">
⇒ (3/11)2 x (11/3)
⇒ 9/121 x 11/3 = 3/11
Example 2: Simplify 7-3 x 3435/3 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 [image]
Sol: [image]
⇒[image]
= 11n+1-n x 31/13 = 341/13
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Example 4: Simplify 73x –2 = 2401 find value of x
Sol: 73x –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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