Question

Найдите значение выражения:
1) (0.8^-2 + 0.6^-2)^-1
2)(5*2^-2 - 20*5^-2) : (4/3)^-2

Answer 1

1.

$(0,8^{-2}+0,6^{-2})^{-1}=((\frac{8}{10})^{-2}+(\frac{6}{10})^{-2})^{-1}=$

$=((\frac{4}{5})^{-2}+(\frac{3}{5})^{-2})^{-1}=((\frac{5}{4})^{2}+(\frac{5}{3})^{2})^{-1}=$

$=(\frac{25}{16}+\frac{25}{9})^{-1}=(\frac{25*9+25*16}{16*9})^{-1}=$

$=(\frac{25*(9+16)}{16*9})^{-1}=(\frac{25*25)}{16*9})^{-1}=$

$=(\frac{625}{144})^{-1}=(\frac{144}{625})^{1}=\frac{144}{625}$

2.

$(5*2^{-2}-20*5^{-2}):(\frac{4}{3})^{-2}=(5*(\frac{1}{2})^2-20*(\frac{1}{5})^2):(\frac{3}{4})^2=$

$=(5*\frac{1}{4}-20*\frac{1}{25}):\frac{9}{16}=$

$=(\frac{5}{4}-\frac{20}{25}):\frac{9}{16}=$

$=(\frac{5}{4}-\frac{4}{5})*\frac{16}{9}=(\frac{5*5}{4*5}-\frac{4*4}{5*4})*\frac{16}{9}=$

$=(\frac{25}{20}-\frac{16}{20})*\frac{16}{9}=(\frac{25}{20}-\frac{16}{20})*\frac{16}{9}=$

$=\frac{9}{20}*\frac{16}{9}=\frac{4}{5}=0,8$