Question

How do you simplify `((9x^6 y^-3 z)/(18xy^3 z^-5))`?

Answer 1

`=(x^(5 ) z ^ 6) / ( 2y^(6)`

Explanation:

`(9x^6y^-3z) / ( 18 x y ^3 z ^-5`

`=(9 * x^6 * y^-3 * z) / ( 18 * x * y ^3 * z ^-5`

`=(cancel9 / cancel18 ) * ( x^6 * y^-3 * z) / ( x * y ^3 * z ^-5`

`=(1/2 ) * ( x^6 * y^-3 * z) / ( x * y ^3 * z ^-5`

• Applying property:
  `color(blue)(a^m / a ^n = a ^(m-n)`

`=(1/2 ) * ( x^(6 - 1)) * ( y^(-3 - 3 )) * ( z ^ ( 1 - ( -5)))`

`=(1/2 ) * x^(5 ) * y^(-6) * z ^ ( (1 + 5))`

`=(1/2 ) x^(5 ) y^(-6) z ^ 6`

`=(x^(5 ) z ^ 6) / ( 2y^(6)`