Question

8 задание с полным решением пж

Answer 1

$\displaystyle \tt \dfrac{0,0027^3\cdot0,0000081^7}{0,03^{29}}=\dfrac{\bigg(\dfrac{27}{10000}\bigg)^3\cdot\bigg(\dfrac{81}{10000000}\bigg)^7}{\bigg(\dfrac{3}{100}\bigg)^{29}}=\dfrac{\dfrac{27^3}{10000^3}\cdot\dfrac{81^7}{10000000^7}}{\dfrac{3^{29}}{100^{29}}}=\\\\\displaystyle \tt \dfrac{\dfrac{27^3\cdot81^7}{10000^3\cdot10000000^7}}{\dfrac{3^{29}}{100^{29}}}=\dfrac{27^3\cdot81^7\cdot100^{29}}{10000^3\cdot10000000^7\cdot3^{29}}=\dfrac{3^9\cdot3^{28}\cdot100^{29}}{100^6\cdot10^{49}\cdot3^{29}}=$

$\\\\ =\displaystyle \tt \dfrac{3^{28}\cdot100^{23}}{10^{49}\cdot3^{20}}=\dfrac{3^8\cdot10^{46}}{10^{49}}=\dfrac{3^8}{10^3}=\dfrac{6561}{1000}=\bold{6,561}$

Ответ: 6,561