Question

How do you simplify `(\frac { 3x ^ { 2} } { y ^ { 2} } ) ^ { 3}`?

Answer 1

See a solution process below:

Explanation:

Use these two rules of exponents to simplify the expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`((3x^2)/y^2)^3 => ((3^color(red)(1)x^color(red)(2))/y^color(red)(2))^color(blue)(3) => (3^(color(red)(1)xxcolor(blue)(3))x^(color(red)(2)xxcolor(blue)(3)))/y^(color(red)(2)xxcolor(blue)(3)) =>`

`(3^3x^6)/y^6 => (27x^6)/y^6`

Answer 2

`(27x^(6))/(y^(6))`

Explanation:

`((3x^2)/(y^2))^3`

Let's apply the power of a quotient

`(3x^2)^3/(y^2)^3`

Now let's use the power of a power rule

`(3^3x^(2^3))/(y^(2^3))`

Now we're going to raise a power to a power, which means we will multiply the powers. So, `x^(3^6)` becomes `x^18`

`(27x^(6))/(y^(6))`