1. मान ज्ञात कीजिए : (i) $3^{-2} = \frac{1}{3^2} = \frac{1}{9}$ (ii) $(-4)^{-2} = \frac{1}{(-4)^2} = \frac{1}{16}$ (iii) $(\frac{1}{2})^{-5} = 2^{5} = 32$ 2. सरल कीजिए और उत्तर को धनात्मक घटांक के रूप में व्यक्त कीजिए। (i) $\frac{(-4)^5}{(-4)^8} = (-4)^{5-8} = (-4)^{-3} = \frac{1}{(-4)^3} = \frac{1}{-64} = -\frac{1}{64}$ (ii) $(\frac{1}{2^3})^2 = (2^{-3})^2 = 2^{-6} = \frac{1}{64}$ (iii) $(-3)^4 \times (\frac{5}{3})^4 = \left((-3) \times \frac{5}{3}\right)^4 = (-5)^4 = 625$ (iv) $\left(\frac{3^{-7}}{3^{-10}}\right) \times 3^{-5} = 3^{-7+10} \times 3^{-5} = 3^{3} \times 3^{-5} = 3^{-2} = \frac{1}{9}$ (v) $2^{-3} \times (-7)^{-3} = \frac{1}{2^3} \times \frac{1}{(-7)^3} = \frac{1}{8} \times \frac{1}{-343} = -\frac{1}{2744}$ 3. मान ज्ञात कीजिए : (i) $(3^{0} + 4^{-1}) \times 2^{2} = (1 + \frac{1}{4}) \times 4 = \frac{5}{4} \times 4 = 5$ (ii) $(2^{-1} \times 4^{-1}) \div 2^{-2} = \left(\frac{1}{2} \times \frac{1}{4}\right) \times 2^{2} = \frac{1}{8} \times 4 = \frac{1}{2}$ (iii) $(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2} = 2^{2} + 3^{2} + 4^{2} = 4 + 9 + 16 = 29$ (iv) $(3^{-1} + 4^{-1} + 5^{-1})^{0} = (\frac{1}{3} + \frac{1}{4} + \frac{1}{5})^{0} = 1$ (v) $\left( \left( \frac{-2}{3} \right)^{-2} \right)^{2} = \left( \left( \frac{3}{-2} \right)^{2} \right)^{2} = \left(\frac{9}{4}\right)^{2} = \frac{81}{16}$ 4. मान ज्ञात कीजिए : (i) $\frac{8^{-1} \times 5^{3}}{2^{-4}} = \frac{\frac{1}{8} \times 125}{\frac{1}{16}} = \frac{125}{8} \times 16 = 125 \times 2 = 250$ (ii) $(5^{-1} \times 2^{-1}) \times 6^{-1} = \frac{1}{5} \times \frac{1}{2} \times \frac{1}{6} = \frac{1}{60}$