Question

What is the simplified form of 15x^8/24y^5 divided by 4x^4/8y^2

Answer 1

(24y^5)/(15x^8) * 4x^4/(8y²) 

Reduce the common factors for the numerator and denominator and multiply the fractions altogether to get... 

24/8 * y^(5 - 2) * 4/15 * 1/x^(8 - 4) 
= 3y³ * 4/15 * 1/x^4 
= 4y³/(5x^4) 

I hope this helps!

Answer 2

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 $\dfrac{5x^4}{4y^3}.$