Question

What's the property to (x/y)^3=x^3/y^3

Answer 1

Answer:

Power of a quotient property

Step-by-step explanation:

It is power of a quotient property, when you have different bases, whose quotient(division) is raised to the same power, it is equal to dividing, each base raised to same power.

Here, x and y are different bases and 3 is the common power to both of them.

In general for any power, say m :

$(\frac{x}{y} )^{m} = \frac{x^{m} }{y^{m}}$

Because, $(\frac{x}{y} )^{m} = \frac{x}{y} \times \frac{x}{y} \times\frac{x}{y}.... m times$

And, $(\frac{x}{y} )^{3} = \frac{x}{y} \times \frac{x}{y} \times\frac{x}{y}$

i.e $(\frac{x}{y} )^{3} = \frac{x^{3} }{y^{3}}$