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

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

Answer Details

The expression can be simplified as follows:

First, we simplify the expression inside the first set of parentheses:

(3x/4 - 1) = (x - 4/3)

Next, we simplify the expression inside the second set of parentheses:

(125^(x - 1)) = (125^x / 125) = (5^x)

Now, we substitute these simplified expressions back into the original expression:

(625(x - 4/3) + 5^x) / (5^(3x - 2))

Finally, we simplify the denominator:

(625(x - 4/3) + 5^x) / (125^(x - 2/3))

This is the simplified form of the expression. Note that this expression can be further simplified, but it depends on the specific values of x.