Question

18x^4y^-7z/4x^9y^4z^-5

Answer 1

The simplified expression to the given expression is

`(18x^4y^(-7)z)/(4x^9y^4z^(-5))=(9z^6)/(2x^5y^(11))`

Explanation:

Given expression is
`(18x^4y^(-7)z)/(4x^9y^4z^(-5))`

To simpify the given expression :

`(18x^4y^(-7)z)/(4x^9y^4z^(-5))`

`=(9x^4y^(-7)z)/(2x^9y^4z^(-5))`

`=(9x^4y^(-7)zx^(-9)y^(-4)z^5)/(2)` ( using the property
`a^(-m)=(1)/(a^m)` )

`=(9x^4.x^(-9)y^(-7)y^(-4)z.z^5)/(2)`

`=(9x^(4-9)y^(-7-4)z^(1+5))/(2)` ( using the property
`a^m.a^n=a^(m+n)` )

`=(9x^(-5)y^(-11)z^(6))/(2)` ( using the property
`a^(-m)=(1)/(a^m)` )

`=(9z^6)/(2x^5y^(11))`

Therefore
`(18x^4y^(-7)z)/(4x^9y^4z^(-5))=(9z^6)/(2x^5y^(11))`

Therefore the simplified expression to the given expression is

`(18x^4y^(-7)z)/(4x^9y^4z^(-5))=(9z^6)/(2x^5y^(11))`