5. Вычислите: a) \(\frac{(8^3)^{-7}}{8^{-23}}\) б) \(\frac{1}{2^{-19}} × \frac{1}{2^{16}}\) в) \(\left(\frac{1}{3}\right)^{-1} - 2^{-4} : 2^{-6}\)

Решение:

1. \( \frac{(8^3)^{-7}}{8^{-23}} = \frac{8^{3 × (-7)}}{8^{-23}} = \frac{8^{-21}}{8^{-23}} = 8^{-21 - (-23)} = 8^{-21 + 23} = 8^2 = 64 \)
2. \( \frac{1}{2^{-19}} × \frac{1}{2^{16}} = 2^{19} × 2^{-16} = 2^{19 + (-16)} = 2^{19-16} = 2^3 = 8 \)
3. \( \left(\frac{1}{3}\right)^{-1} - 2^{-4} : 2^{-6} = 3 - 2^{-4 - (-6)} = 3 - 2^{-4 + 6} = 3 - 2^2 = 3 - 4 = -1 \)

Ответ: а) 64; б) 8; в) -1.