Question

if we multiply a fraction by itself and divide the product by its reciprocal then we get the fraction 512/27. what is the original fraction... plz hep me...

Answer 1

Let numerator of fraction be x
and denominator of it be y
fraction will be x/y

(x/y)*(x/y)/(y/x)=512/27
(x^2/y^2)/(y/x)=512/27
x^3/y^3=512/27
x/y=8/3

original fraction=x/y
x/y=8/3

Answer 2

Answer:

$\frac{x}{y}=\frac{8}{3}$

Step-by-step explanation:

Let the numerator be x

Let the denominator be y

Fraction : $\frac{x}{y}$

Product of fraction with itself = $\frac{x}{y} \times \frac{x}{y} =\frac{x^2}{y^2}$

Reciprocal of fraction : $\frac{y}{x}$

Now divide the product by its reciprocal

So, $\frac{\frac{x^2}{y^2}}{\frac{y}{x}}$

$\frac{x^2}{y^2}\times \frac{x}{y}$

$\frac{x^3}{y^3}$

Now we are given  that we get the fraction 512/27.

So, $\frac{x^3}{y^3}=\frac{512}{27}$

$\frac{x}{y}=\sqrt[3]{\frac{512}{27}}$

$\frac{x}{y}=\frac{8}{3}$

Hence  the original fraction is  $\frac{x}{y}=\frac{8}{3}$