<s>[INST] Indices/Exponents: Simplify the following expression I've been asked to simplify this expressing it with positive indices/exponents. Could someone please show me in steps how to do this? The answer is shown next to it. Thanks a lot. 
$$\dfrac{{(\large a^\frac{-5}{2})}^2 b^2}{\large {a}^3(b^\frac{1}{4})^6} = \dfrac{b^\frac{1}{2}}{a^8}$$
 [/INST] $$ \begin{eqnarray*}  
\left(  a^{-\frac 52} \right)^2 = a^{-5}
\\ \frac 1{a^3}=a^{-3}
\\ \dfrac 1 { \left(  b^{\frac 14} \right)^6}=b^{-\frac 32}
\end{eqnarray*} $$
so 
$$ \begin{eqnarray*}  
\dfrac {\left(  a^{-\frac 52} \right)^2b^2 }{a^3\left(  b^{\frac 14} \right)^6}
&=a^{-5}a^{-3}b^2 b^{-\frac 32}
\\&=a^{-8}b^\frac 12
\end{eqnarray*} $$
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