Question

How do you multiply and simplify `(\frac { 2x y ^ { 2} \cdot - 2x ^ { 0} y ^ { 2} } { - 2x ^ { - 1} y ^ { 0} } ) ^ { 3}`?

Answer 1

The answer is `8x^6y^12`.

Explanation:

`((2xy^2*(-2x^0 y^2))/(-2x^-1 y^0))^3`

First, remember that anything raised to the 0th power is equal to `1`. So start by canceling out all the terms that are raised to `0`.

`((2xy^2 * (-2(1)y^2))/(-2x^-1(1)))^3`

`((2xy^2 * (-2y^2))/(-2x^-1))^3`

Multiply the numerator by adding the exponent of like terms. Don't forget the negative sign!

`((-4xy^4)/(-2x^-1))^3`

`((2xy^4)/(x^-1))^3`

Remember that anything raised to the `-1` is basically a reciprocal, so:

`x^-1 = 1/x`

Therefore:

`((2xy^4)/(1/x))^3`

which is

`(2xy^4 * x)^3`

`(2x^2y^4)^3`

Distribute the exponent

`2^3 * x^(2 * 3) * y^ (4*3)`

`= 8x^6y^12`