\( 8^{-2} \times (\frac{1}{5})^6 \)
\( = (2^3)^{-2} \times 5^{-6} \)
\( = 2^{-6} \times 5^{-6} \)
\( = (2 \times 5)^{-6} = 10^{-6} \)
\( (-\frac{5}{4})^{-6} \times (\frac{7}{5})^{-6} \)
\( = (-\frac{5}{4} \times \frac{7}{5})^{-6} \)
\( = (-\frac{7}{4})^{-6} = (-\frac{4}{7})^6 \)
\( (\frac{2}{5})^3 \times (\frac{2}{5})^{-9} \)
\( = (\frac{2}{5})^{3-9} \)
\( = (\frac{2}{5})^{-6} = (\frac{5}{2})^6 \)
\( \sqrt{\frac{9}{25}} \times (\frac{3}{5})^{-14} \times \frac{27}{125} \)
\( = \frac{3}{5} \times (\frac{3}{5})^{-14} \times (\frac{3}{5})^3 \)
\( = (\frac{3}{5})^{1-14+3} \)
\( = (\frac{3}{5})^{-10} = (\frac{5}{3})^{10} \)
\( \frac{(-11/3)^9}{(-5/2)^9} \)
\( = (\frac{-11/3}{-5/2})^9 \)
\( = (\frac{11}{3} \times \frac{2}{5})^9 = (\frac{22}{15})^9 \)
\( \frac{(-5/7)^{10}}{(5/7)^6} \)
بما أن دليل القوة 10 زوجي: \( (-5/7)^{10} = (5/7)^{10} \)
\( = (5/7)^{10-6} = (5/7)^4 \)
\( A = (\frac{3}{5})^{-12} \times (\frac{3}{5})^{18} \)
\( = (\frac{3}{5})^{-12+18} \)
\( = (\frac{3}{5})^6 \)
\( B = (-\frac{1}{2})^{18} \times (\frac{1}{2})^{19} \)
\( = (\frac{1}{2})^{18} \times (\frac{1}{2})^{19} \)
\( = (\frac{1}{2})^{18+19} = (\frac{1}{2})^{37} \)
\( C = [(\frac{1}{2})^3]^{-2} \)
\( = (\frac{1}{2})^{3 \times -2} \)
\( = (\frac{1}{2})^{-6} = 2^6 \)
\( D = (\frac{11}{5})^{-17} \times \frac{11}{5} \)
\( = (\frac{11}{5})^{-17+1} \)
\( = (\frac{11}{5})^{-16} = (\frac{5}{11})^{16} \)
\( E = (\frac{4}{3})^{18} \times (\frac{9}{16})^{-19} \)
\( = (\frac{4}{3})^{18} \times [(\frac{4}{3})^{-2}]^{-19} \)
\( = (\frac{4}{3})^{18} \times (\frac{4}{3})^{38} \)
\( = (\frac{4}{3})^{56} \)
\( F = (5^4 \times 3^{-2})^4 \times 3^{24} \)
\( = 5^{16} \times 3^{-8} \times 3^{24} \)
\( = 5^{16} \times 3^{16} \)
\( = (5 \times 3)^{16} = 15^{16} \)
\( A = (\frac{9}{5})^{-11} \times (\frac{9}{5})^{20} \)
\( = (\frac{9}{5})^{-11+20} = (\frac{9}{5})^9 \)
\( B = (\frac{7}{5})^{29} \times (-\frac{7}{5})^{-8} \)
\( = (\frac{7}{5})^{29} \times (\frac{7}{5})^{-8} \)
\( = (\frac{7}{5})^{29-8} = (\frac{7}{5})^{21} \)
\( C = \frac{(7/3)^{24}}{(7/3)^{14}} \)
\( = (7/3)^{24-14} = (7/3)^{10} \)
\( D = \frac{(-3/5)^{-2} \times (5/3)^3}{(1/2)^5} \)
\( = \frac{(5/3)^2 \times (5/3)^3}{(1/2)^5} \)
\( = \frac{(5/3)^5}{(1/2)^5} = (\frac{10}{3})^5 \)
\( E = (\frac{27}{8})^{-2} \times (\frac{3}{2})^4 \)
\( = [(\frac{3}{2})^3]^{-2} \times (\frac{3}{2})^4 \)
\( = (\frac{3}{2})^{-6} \times (\frac{3}{2})^4 = (\frac{3}{2})^{-2} \)
\( F = \frac{0,001^4 \times 1000^{-2}}{100^{-3} \times 0,01^{-5}} \)
\( = \frac{(10^{-3})^4 \times (10^3)^{-2}}{(10^2)^{-3} \times (10^{-2})^{-5}} \)
\( = \frac{10^{-12} \times 10^{-6}}{10^{-6} \times 10^{10}} = 10^{-22} \)
\( (-6,17)^{147} \times (-6,17)^{23} \)
\( = (-6,17)^{147+23} \)
\( = (-6,17)^{170} = (6,17)^{170} \)
\( (-0,9)^{-2009} \times (\frac{307}{333})^{-2009} \)
\( = (-0,9 \times \frac{307}{333})^{-2009} \)
\( = (-\frac{9}{10} \times \frac{307}{333})^{-2009} \)
\( [(\frac{5}{7})^{-120}]^4 \)
\( = (\frac{5}{7})^{-120 \times 4} = (\frac{5}{7})^{-480} \)
\( = (\frac{7}{5})^{480} \)
\( \frac{(-19)^{167}}{(-19)^{57}} \)
\( = (-19)^{167-57} = (-19)^{110} \)
\( = 19^{110} \)
\( \frac{(-3,14)^{-219}}{(3,14)^{124}} \times \frac{1}{(-3)^{-343}} \)
\( = \frac{-(3,14)^{-219}}{(3,14)^{124}} \times (-3)^{343} \)
\( = -(3,14)^{-343} \times (-3)^{343} = (3,14 \times 3)^{-343} \)
\( -(2^3)^5 \)
\( = -(2)^{3 \times 5} \)
\( = -2^{15} \)