Question

Can someone show me the answer and maybe the work

Answer 1

Answer:

Solving the expression \frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3} we get $\mathbf{\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}}$

Step-by-step explanation:

We need to solve the expression:

$\frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3}$

We know the exponent rule: $(a^n)^m = a^{nm}$

$\frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3}\\\\=\frac{y^2z^{\frac{1}{4}} }{z^{\frac{3}{2}}.x^3y^{\frac{9}{2} }}$

Now, another exponent rule says that: $\frac{a^m}{a^n}=a^{m-n}$

$=\frac{y^{2-\frac{9}{2}} z^{\frac{1}{4}-\frac{3}{2} } }{x^3}\\=\frac{y^{\frac{4-9}{2}} z^{\frac{1-3*2}{4} } }{x^3}\\=\frac{y^{\frac{-5}{2}}z^{\frac{-5}{4} } }{x^3}$

We also know that: $a^{-m}=\frac{1}{a^m}$

=$\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}$

So, solving the expression \frac{y^2z^{\frac{1}{4}} }{(z^{\frac{1}{2}}.xy^{\frac{3}{2}})^3} we get $\mathbf{\frac{1}{y^{\frac{5}{2} }x^3z^{\frac{5}{4} }}}$