Surds and Indices: Solved Examples

Directions: Solve the following questions applying the various indices and surds formulas.
Example 1: Simplify (27/1331)2/3 x (121/9)1/2
Pml Web Banner
Sol:<em>Indices and Surds Solved</em>
⇒ (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 Indices and Surds Solved
Sol: Indices and Surds Solved
Indices and Surds Solved
= 11n+1-n x 31/13 = 341/13
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
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
bimtech