Evaluate the following expressions: (6^-2)^-1 = ? 7^-1 * 7^-3 = ? 7^-1 / 7^-3 = ? (3^2 * 2^3) / 6^2 = ? (1/2)^-2 * 2^-3 = ?

Question

Accepted Answer

\( (6^{-2})^{-1} = 6^{(-2) \cdot (-1)} = 6^2 = 36 \)
\( 7^{-1} \cdot 7^{-3} = 7^{-1 + (-3)} = 7^{-4} = \frac{1}{7^4} = \frac{1}{2401} \)
\( 7^{-1} : 7^{-3} = 7^{-1 - (-3)} = 7^{-1 + 3} = 7^2 = 49 \)
\( \frac{3^2 \cdot 2^3}{6^2} = \frac{9 \cdot 8}{(3 \cdot 2)^2} = \frac{72}{3^2 \cdot 2^2} = \frac{72}{9 \cdot 4} = \frac{72}{36} = 2 \)
\( \left(\frac{1}{2}\right)^{-2} \cdot 2^{-3} = (2^{-1})^{-2} \cdot 2^{-3} = 2^{(-1) \cdot (-2)} \cdot 2^{-3} = 2^2 \cdot 2^{-3} = 2^{2 + (-3)} = 2^{-1} = \frac{1}{2} \)

Ответ: 36; \(\frac{1}{2401}\); 49; 2; \(\frac{1}{2}\).