Question

Вычислите:
(4⁵ ∙ 16⁻⁸)² / 64⁻⁷

Answer 1

$\displaystyle\bf\\\frac{\Big(4^{5} \cdot 16^{-8} \Big)^{2} }{64^{-7} } =\frac{\Big[\Big(2^{2}\Big) ^{5}\cdot\Big(2^{4}\Big)^{-8}\Big]^{2}}{\Big(2^{6} \Big)^{-7} } =\frac{\Big[(2^{10} \cdot 2^{-32}\Big]^{2}}{2^{-42} } =\\\\\\=\frac{\Big(2^{10-32} \Big)^{2} }{2^{-42} } =\frac{\Big(2^{-22}\Big)^{2} }{2^{-42} } =\frac{2^{-44} }{2^{-42} } =2^{-44-(-42)} =2^{-44+42} =\\\\\\=2^{-2} =\frac{1}{2^{2} } =\frac{1}{4} =0,25$