Answer :

Answer:

The simplified expression to the given expression is

[tex]\frac{18x^4y^{-7}z}{4x^9y^4z^{-5}}=\frac{9z^6}{2x^5y^{11}}[/tex]

Step-by-step explanation:

Given expression is [tex]\frac{18x^4y^{-7}z}{4x^9y^4z^{-5}}[/tex]

To simpify the given expression :

[tex]\frac{18x^4y^{-7}z}{4x^9y^4z^{-5}}[/tex]

[tex]=\frac{9x^4y^{-7}z}{2x^9y^4z^{-5}}[/tex]

[tex]=\frac{9x^4y^{-7}zx^{-9}y^{-4}z^5}{2}[/tex] ( using the property [tex]a^{-m}=\frac{1}{a^m}[/tex] )

[tex]=\frac{9x^4.x^{-9}y^{-7}y^{-4}z.z^5}{2}[/tex]

[tex]=\frac{9x^{4-9}y^{-7-4}z^{1+5}}{2}[/tex] ( using the property [tex]a^m.a^n=a^{m+n}[/tex] )

[tex]=\frac{9x^{-5}y^{-11}z^{6}}{2}[/tex] ( using the property [tex]a^{-m}=\frac{1}{a^m}[/tex] )

[tex]=\frac{9z^6}{2x^5y^{11}}[/tex]

Therefore [tex]\frac{18x^4y^{-7}z}{4x^9y^4z^{-5}}=\frac{9z^6}{2x^5y^{11}}[/tex]

Therefore the simplified expression to the given expression is

[tex]\frac{18x^4y^{-7}z}{4x^9y^4z^{-5}}=\frac{9z^6}{2x^5y^{11}}[/tex]