Question

How do you simplify `(x^-1y^-2z^3)^-2 (x^2y^-4z^6)`?

Answer 1

Use the following three properties:

`(x*y*z*...)^a=x^a*y^a*z^a*...`

`(x^a)^b=x^(a*b)`

`x^a*x^b=x^(a+b)`

Answer is:

`x^4y^0z^0`

Explanation:

`(x^-1y^-2z^3)^-2(x^2y^-4z^6)`

• Use `(x*y*z*...)^a=x^a*y^a*z^a*...`

`(x^-1)^-2(y^-2)^-2(z^3)^-2x^2y^-4z^6`

• Use `(x^a)^b=x^(a*b)`

`x^(-1*(-2))y^(-2*(-2))z^(3*(-2))x^2y^-4z^6`

`x^2y^4z^-6x^2y^-4z^6`

• Use `x^a*x^b=x^(a+b)`

`x^(2+2)y^(4+(-4))z^(-6+6)`

`x^4y^0z^0`

Note: don't say that `y^0=1` and `z^0=1` because that is not true for `y=0` and `z=0`

If you wish you can use `x^-a=1/x^a` but it's easier without it.