Exponent Examples with Questions and Solutions

Directions for questions 1 to 5: Applying the various rules of exponents and powers solve the following questions.

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Example 1: Simplify (8/343)^2/3 x (49/16)^1/2

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 27^5/3 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) = 2^n+1-n = 2

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Example 4: Simplify 2^2x-3 = 2048 fid value of x

Sol: 2^2x-3 = 2¹¹

So 2x - 3 = 11

⇒ 2x = 10

⇒ x = 7

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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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