1. Вычислите: 1) 12⁻²; 2) 3⁻⁴; 3) (−2)⁻⁶; 4) (−5)⁻³; 5) 100⁻¹; 6) (−1/8)⁻¹; 7) (2/3)⁻³; 8) (−7/9)⁻²; 9) (1 2/3)⁻¹.

Question

Вопрос:

1. Вычислите: 1) 12⁻²; 2) 3⁻⁴; 3) (−2)⁻⁶; 4) (−5)⁻³; 5) 100⁻¹; 6) (−1/8)⁻¹; 7) (2/3)⁻³; 8) (−7/9)⁻²; 9) (1 2/3)⁻¹.

Accepted Answer

По правилу \(a^{-n}=\frac{1}{a^n}\): \(12^{-2}=\frac{1}{12^2}=\frac{1}{144}\).
\(3^{-4}=\frac{1}{3^4}=\frac{1}{81}\).
\((-2)^{-6}=\frac{1}{(-2)^6}=\frac{1}{64}\).
\((-5)^{-3}=\frac{1}{(-5)^3}=-\frac{1}{125}\).
\(100^{-1}=\frac{1}{100}\).
\(\left(-\frac{1}{8}\right)^{-1}=-8\).
\(\left(\frac{2}{3}\right)^{-3}=\left(\frac{3}{2}\right)^3=\frac{27}{8}\).
\(\left(-\frac{7}{9}\right)^{-2}=\left(-\frac{9}{7}\right)^2=\frac{81}{49}\).
\(1\frac{2}{3}=\frac{5}{3}\), поэтому \(\left(1\frac{2}{3}\right)^{-1}=\frac{3}{5}\).

Ответ: 1) \(\frac{1}{144}\); 2) \(\frac{1}{81}\); 3) \(\frac{1}{64}\); 4) \(-\frac{1}{125}\); 5) \(\frac{1}{100}\); 6) \(-8\); 7) \(\frac{27}{8}\); 8) \(\frac{81}{49}\); 9) \(\frac{3}{5}\).