((frac (5)/(6))^10)(((5)/(6))^12)=(81)/(10000) (0.0001^-2times 10000^8)/(1000^3):(8^3times 2^-5)/((4times 2^3))^(-7times 16^-9)

لنقم بحل المعادلة الثانية:<br /><br />$\frac {0.0001^{-2}\times 10000^{8}}{1000^{3}}:\frac {8^{3}\times 2^{-5}}{(4\times 2^{3})^{-7}\times 16^{-9}}$<br /><br />نبدأ بحل الجزء الأول من المعادلة:<br /><br />$0.0001^{-2} = (10^{-4})^{-2} = 10^{8}$<br /><br />$10000^{8} = (10^{4})^{8} = 10^{32}$<br /><br />$1000^{3} = (10^{3})^{3} = 10^{9}$<br /><br />لذلك، يصبح الجزء الأول من المعادلة:<br /><br />$\frac {10^{8} \times 10^{32}}{10^{9}} = 10^{31}$<br /><br />الآن، ننتقل إلى الجزء الثاني من المعادلة:<br /><br />$8^{3} = 512$<br /><br />$2^{-5} = \frac{1}{32}$<br /><br />$(4 \times 2^{3})^{-7} = (4 \times 8)^{-7} = 32^{-7} = \frac{1}{32^{7}}$<br /><br />$16^{-9} = \frac{1}{16^{9}}$<br /><br />لذلك، يصبح الجزء الثاني من المعادلة:<br /><br />$\frac {512 \times \frac{1}{32}}{\frac{1}{32^{7}} \times \frac{1}{16^{9}}} = \frac {512 \times 32}{32^{7} \times 16^{9}} = \frac {512 \times 32}{32^{7} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times 16^{9}} = \frac {512}{32^{6} \times