Answer:
\(\frac{4y^3}{5x^4}\)
Step-by-step explanation:
Given phrase,
24 y to the fifth power over 15 x to the eighth power divided by 8 y squared over 4 x to the fourth power
\(\implies \frac{24y^5}{15x^8}\div \frac{8y^2}{4x^4}\)
\(=\frac{24y^5}{15x^8}\times \frac{4x^4}{8y^2}\) ( Division of fractions )
\(=\frac{24y^5\times 4x^4}{15x^8\times 8y^2}\) ( Multiplication of fractions )
\(=\frac{96x^4y^5}{120x^8y^2}\)
\(=\frac{4}{5} x^4y^5 x^{-8} y^{-2}\) ( \(a^m=\frac{1}{a^{-m}}\) )
\(=\frac{4}{5}x^{-4}y^{3}\) ( \(a^m.a^n=a^{m+n}\) )
\(=\frac{4y^3}{5x^4}\)