find x from the question
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81⁻² ÷ 729¹⁻ˣ = 9²ˣ
=> [(3)⁴]⁻² ÷ (3)⁶⁽¹⁻ˣ⁾ = [(3)²]²ˣ
=> 3⁻⁸ ÷ (3)⁶⁻⁶ˣ = (3)⁴ˣ
=> 3⁻⁸ × (3)⁶ˣ⁻⁶ = (3)⁴ˣ
[ ÷ is same as × by reciprocal]
=> 3⁽⁻⁸⁺⁶ˣ⁻⁶ = (3)⁴ˣ
=> 3⁶ˣ⁻¹⁴ = (3)⁴ˣ [ as base 3 is common on both sides, we can equate the exponents ]
=> 6x - 14 = 4x
=> 6x - 4x = 14
=> 2x = 14
=> x = 7
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