Answer: The required simplified form is \(\dfrac{5x^4}{4y^3}.\)
Step-by-step explanation: We are given to find he simplified form of the following division :
\(\dfrac{15x^8}{24y^5}~~~\textup{divided by}~~~\dfrac{4x^4}{8y^2}.\)
We know the following method :
\(\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}.\)
Also, we note the following rule of exponents :
\(\dfrac{x^a}{x^b}=x^{a-b}.\)
The simplification of the given division is as follows :
\(\dfrac{15x^8}{24y^5}~~~\textup{divided by}~~~\dfrac{4x^4}{8y^2}\\\\\\=\dfrac{15x^8}{24y^5}\div \dfrac{4x^4}{8y^2}\\\\\\=\dfrac{15x^8}{24y^5}\times\dfrac{8y^2}{4x^4}\\\\\\=\dfrac{5\times2}{8}\times\dfrac{x^{8-4}}{y^{5-2}}\\\\\\=\dfrac{5x^4}{4y^3}.\)
Thus, the required simplified form is \(\dfrac{5x^4}{4y^3}.\)
