Simplify \(\frac{ 625(\frac{3x}{4} - 1) + 125^{(x - 1)} }{5^{(3x - 2)}}\)

Explanation

\(\frac{625(\frac{3x}{4} - 1) + 125^{(x - 1)}}{5^{(3x - 2)}}\)

\(\frac{5^4(\frac{3x}{4} - 1) + 5^{3(x - 1)}}{5^{(3x - 2)}}\)

\(\frac{5^{3x - 4} + 5^{3x - 3}}{5^{3x} \times 5^{-2}}\)

= \(\frac{5^{3x}(5^{-4} + 5^{-3})}{5^{3x} \times 5{-2}}\)

= \(\frac{5^{-3}(5^{-1} + 1)}{5^{-2}}\)

= 5\(^{-1} (5^{-1} + 1)\)

= \(\frac{1}{5}(\frac{1}{5} + \frac{1}{1}\))

= \(\frac{1}{5} \times \frac{6}{5} = \frac{6}{25}\)