Question

How do you simplify `(xy)^-3/(x^-5y)^3`?

Answer 1

`= color(blue)(x ^12 y ^(-6)`

Explanation:

`(xy)^-3 / (x^-5 y)^3`

• As per property:
  `color(blue)(a^m)^n = color(blue)(a^(mn)`

Applying the above property to the expression provided:

`(xy)^-3 / (x^-5 y)^3 = (x^ -3 y^-3) / (x^ ((-5 * 3) ) * y^3)`

`= (x^-3y^-3) / ((x^-15)* y^3`

• As per property:
  `color(blue)(a^m / a^n = a^(m-n)`
  Applying the above to `x` and `y`:

`(x^-3y^-3) / (x^-15y^3)= x^ (-3 - (- 15)) * y ^ ((-3 -3))`

`= x ^ ((- 3 + 15 )) y ^(-6)`

`= x ^12 y ^(-6)`

• As per property:
  `color(blue)(a^-1 = 1 /a`

`= x ^12 y ^(-6) = x ^12 / y ^6`