Question

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

Answer 1

Power of a quotient property

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 :

`((x)/(y) )^(m) = (x^(m) )/(y^(m))`

Because,
`((x)/(y) )^(m) = (x)/(y) * (x)/(y) *(x)/(y).... m times`

And,
`((x)/(y) )^(3) = (x)/(y) * (x)/(y) *(x)/(y)`

i.e
`((x)/(y) )^(3) = (x^(3) )/(y^(3))`