Sievennä lauseke
$$\left[ \frac{(a^2b^{-2}c)^{-3}:\left(c^2\cdot (ab^{-2})^0 \cdot a^{-4}\right)}
{\left((c^{-1}\cdot a^3)^{-1}:a^2\right)^3(ab^2c^{-3})^3} \right]^2.$$
Ratkaisu
Neliöin aina muutokset edellisestä:
\begin{align*}
\left[ \frac{(a^2b^{-2}c)^{-3}: \left(c^2\cdot\boxed{ (ab^{-2})^0 } \cdot a^{-4}\right)}
{\left((c^{-1}\cdot a^3)^{-1}:a^2\right)^3(ab^2c^{-3})^3} \right]^2
&=
\left[ \frac{\boxed{ (a^2b^{-2}c)^{-3}} :\left(c^2\cdot 1 \cdot a^{-4}\right)}
{\left(\boxed{ (c^{-1}\cdot a^3)^{-1}} :a^2\right)^3 \boxed{ (ab^2c^{-3})^3 }} \right]^2
\\
&=
\left[ \frac{ \boxed{ a^{-6}b^{6}c^{-3}:\left(c^2 a^{-4}\right)} }
{ \left( \boxed{ c^{1} a^{-3}:a^2 }\right)^3 a^3b^6c^{-9}} \right]^2 \\
&=
\left[ \frac{ \boxed{a^{-6-(-4)} }\cancel{b}^{6}\boxed{ c^{ -3-2} } }
{\boxed{ \left(c^{1} a^{-5}\right)^3 } a^3\cancel{b}^6c^{-9}} \right]^2 \\
&=
\left[ \frac{a^{-2}c^{-5}}
{\boxed{ \left(c^{3} a^{-15}\right) a^3c^{-9}}} \right]^2 \\
&=
\left( \frac{a^{-2}c^{-5}}
{ c^{-6} a^{-12} } \right)^2 \\
&=
\left( a^{-2-(-12)}c^{-5-(-6)} \right)^2 \\
&=
\left( a^{10}c \right)^2,
\end{align*}
mikä on sama kuin laskimen antama. “Virallinen” vastaus oli $c^2\dots$
Sama pdf-tiedostona: vast.pdf