Question

Найдите значение выражения: (a^-3)^3 / a^-2 - a^-3, при a=1/3

Answer 1

$a=\dfrac{1}{3}\\\\\\1)\ \ \dfrac{(a^{-3})^3}{a^{-2}-a^{-3}}=\dfrac{a^{-9}}{\frac{1}{a^2}-\frac{1}{a^3}}=\dfrac{\frac{1}{a^9}}{\frac{a-1}{a^3}}=\dfrac{a^3}{a^9\cdot (a-1)}=\dfrac{1}{a^6\cdot (a-1)}=\\\\\\=\dfrac{1}{\frac{1}{3^6}\cdot (\frac{1}{3}-1)}=\dfrac{3^6}{-\frac{2}{3}}=-\dfrac{3^7}{2}=-\dfrac{2187}{2}=-1093,5$

$2)\ \ \ \dfrac{(a^{-3})^3}{a^{-2}}-a^{-3}=\dfrac{a^{-9}}{\frac{1}{a^2}}-\dfrac{1}{a^3}=\dfrac{\frac{1}{a^9}}{\frac{1}{a^2}}-\dfrac{1}{a^3}}=\dfrac{a^2}{a^9}-\dfrac{1}{a^3}=\dfrac{1}{a^7}-\dfrac{1}{a^3}=\\\\\\=\dfrac{a^4-1}{a^7}=\dfrac{\frac{1}{3^4}-1}{\frac{1}{3^7}}=-\dfrac{1-3^4}{\frac{3^4}{3^7}}=3^3\cdot (1-3^4)=27\cdot (1-81)=\\\\\\=-27\cdot 80=-2160$