Vereenvoudig die volgende uitdrukkings (1) \( \frac{4^{x} \cdot 2^{x-2}}{8^{x-1}} \)
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Om \( \frac{4^{x} \cdot 2^{x-2}}{8^{x-1}} \) te vereenvoudig, kan ons almal in terme van 2 herskryf. Onthou dat \( 4 = 2^2 \) en \( 8 = 2^3 \). As ons dit nou substitueer, kry ons: \[ \frac{(2^2)^{x} \cdot 2^{x-2}}{(2^3)^{x-1}} = \frac{2^{2x} \cdot 2^{x-2}}{2^{3(x-1)}} \] Die teller kan saamgevoeg word: \[ = \frac{2^{2x + (x-2)}}{2^{3x - 3}} = \frac{2^{3x - 2}}{2^{3x - 3}} \] Deur die eksponente in die teller en noemer af te trek: \[ = 2^{(3x - 2) - (3x - 3)} = 2^{1} = 2 \] So, die vereenvoudigde vorm is \( 2 \).