Answer:
Solving the expression \frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3} we get [tex]\mathbf{\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}}[/tex]
Step-by-step explanation:
We need to solve the expression:
[tex]\frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3}[/tex]
We know the exponent rule: [tex](a^n)^m = a^{nm}[/tex]
[tex]\frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3}\\\\=\frac{y^2z^{\frac{1}{4}} }{z^{\frac{3}{2}}.x^3y^{\frac{9}{2} }}[/tex]
Now, another exponent rule says that: [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
[tex]=\frac{y^{2-\frac{9}{2}} z^{\frac{1}{4}-\frac{3}{2} } }{x^3}\\=\frac{y^{\frac{4-9}{2}} z^{\frac{1-3*2}{4} } }{x^3}\\=\frac{y^{\frac{-5}{2}}z^{\frac{-5}{4} } }{x^3}[/tex]
We also know that: [tex]a^{-m}=\frac{1}{a^m}[/tex]
=[tex]\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}[/tex]
So, solving the expression \frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3} we get [tex]\mathbf{\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}}[/tex]
