Question - Simplifying a Fractional Expression

First, simplify the denominator:

(8x²y³)³ = 8³(x²)³(y³)³ = 512x^{6}y^{9}

Now, the expression becomes:

\(\frac{50x^{-3}y^{14}}{512x^{6}y^{9}}\)

Next, simplify by dividing the coefficients and subtracting the exponents:

\(=\frac{50}{512}x^{-3-6}y^{14-9}\)

Which simplifies to:

\(\frac{25}{256}x^{-9}y^{5}\)

Finally, rewrite with positive exponents:

\(\frac{25y^{5}}{256x^{9}}\)