Please solve it and please do elaborate the solution.
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-42
Step-by-step explanation:
7²ⁿ⁺³ - (49)ⁿ⁺² / [(343)ⁿ⁺¹]²/³
//Solve Denominator part
//remember (xᵃ)ᵇ = xᵃᵇ
(343)ⁿ⁺¹]²/³ = (343)²⁽ⁿ⁺¹⁾/³ = (7³)²⁽ⁿ⁺¹⁾/³= 7⁶⁽ⁿ⁺¹⁾/³ = 7²⁽ⁿ⁺¹⁾ = 7²ⁿ⁺²
//substitute the values back
7²ⁿ⁺³ - (7²)ⁿ⁺² / 7²ⁿ⁺²
//separate the numerator items
= 7²ⁿ⁺³ / 7²ⁿ⁺² - 7²ⁿ⁺⁴/7²ⁿ⁺²
//remember xᵃ/xᵇ = xᵃ⁻ᵇ
= 7²ⁿ⁺³ ⁻ ⁽²ⁿ⁺²⁾ - 7²ⁿ⁺⁴ ⁻ ⁽²ⁿ⁺²⁾
= 7²ⁿ⁺³ ⁻ ²ⁿ⁻² - 7²ⁿ⁺⁴ ⁻²ⁿ⁻²
= 7¹ - 7²
= 7 - 49 = -42.
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