Exponents: Solved Examples

Directions for questions 1 to 5: Applying the various rules of exponents and powers solve the following questions.
Example 1: Simplify (8/343)2/3 x (49/16)1/2
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Sol: (23/73)2/3 x (72/42)1/2
(2/7)2 x (7/4)
(4/49) x (7/4) = (1/7)
 
Example 2: Simplify 3-3 x 275/3 x (81)-3/4
Sol: 3-3 x (33)5/3 x (34)-3/4
(1/33) x 35 x 3-3
(1/33) x 35 x (1/33) = 1/3
 
Example 3: Simplify (2n+3) + 3 x (2n+1) / 5 x (2n+1) - 2n x 3
Sol: 2n+1(4+3) / 2n (5 x 2 - 3)
2n+1(7) / 2n(7) = 2n+1-n = 2
 
Example 4: Simplify 22x-3 = 2048 fid value of x
Sol: 22x-3 = 211
So 2x - 3 = 11
⇒ 2x = 10
⇒ x = 7
 
Example 5: &redic; (5/3)6x-4 = 81/375 find value of x
Sol: (5/3)3x-2 = 34/3x53 = (3/5)3
(5/3)3x-2 = (5/3)-3
3x-2 = -3 ⇒ 3x -1 ⇒ x = -1/3
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