1) a) 3^{7} \(\cdot\) 3^{-6}; б) 7^{-9} \(\cdot\) 7^{8}; в) \(\left\)\(\frac{1}{5}\right\)^{-7} \(\cdot\) \(\left\)\(\frac{1}{5}\right\)^{6}; г) \(\left\)\(\frac{1}{4}\right\)^{14} \(\cdot\) \(\left\)\(\frac{1}{4}\right\)^{-16}

Решение:

1. \( 3^{7} \cdot 3^{-6} = 3^{7+(-6)} = 3^{1} = 3 \)
2. \( 7^{-9} \cdot 7^{8} = 7^{-9+8} = 7^{-1} = \frac{1}{7} \)
3. \( \left(\frac{1}{5}\right)^{-7} \cdot \left(\frac{1}{5}\right)^{6} = \left(\frac{1}{5}\right)^{-7+6} = \left(\frac{1}{5}\right)^{-1} = 5 \)
4. \( \left(\frac{1}{4}\right)^{14} \cdot \left(\frac{1}{4}\right)^{-16} = \left(\frac{1}{4}\right)^{14+(-16)} = \left(\frac{1}{4}\right)^{-2} = 4^{2} = 16 \)

Ответ: 1) а) 3; б) \(\frac{1}{7}\); в) 5; г) 16.