4. Вычислить: 1) ((5³)-4) / 5⁻¹¹ 2) 5⁻⁷ · (5⁵)² 3) (5⁻³,5⁻⁹) / 5⁻¹¹ 4) (6 · 10²)³ · (13 · 10⁻⁵) 5) 7⁻³,⁷¹³ / 7⁸ 6) (2⁴)⁻⁶ / 2⁻²⁷ 7) 3⁻⁸ · (3⁶)² 8) (4⁸ · 11¹⁰) / 44⁸

Question

Вопрос:

Ответ:

Accepted Answer

\( \frac{(5^3)^{-4}}{5^{-11}} = \frac{5^{3 \cdot (-4)}}{5^{-11}} = \frac{5^{-12}}{5^{-11}} = 5^{-12 - (-11)} = 5^{-12+11} = 5^{-1} = \frac{1}{5} \)
\( 5^{-7} \cdot (5^5)^2 = 5^{-7} \cdot 5^{5 \cdot 2} = 5^{-7} \cdot 5^{10} = 5^{-7+10} = 5^3 = 125 \)
\( \frac{5^{-3} \cdot 5^{-9}}{5^{-11}} = \frac{5^{-3+(-9)}}{5^{-11}} = \frac{5^{-12}}{5^{-11}} = 5^{-12 - (-11)} = 5^{-12+11} = 5^{-1} = \frac{1}{5} \)
\( (6 \cdot 10^2)^3 \cdot (13 \cdot 10^{-5}) = 6^3 \cdot (10^2)^3 \cdot 13 \cdot 10^{-5} = 216 \cdot 10^{2 \cdot 3} \cdot 13 \cdot 10^{-5} = 216 \cdot 10^6 \cdot 13 \cdot 10^{-5} = 216 \cdot 13 \cdot 10^{6+(-5)} = 2808 \cdot 10^1 = 28080 \)
\( \frac{7^{-3} \cdot 7^{13}}{7^8} = \frac{7^{-3+13}}{7^8} = \frac{7^{10}}{7^8} = 7^{10-8} = 7^2 = 49 \)
\( \frac{(2^4)^{-6}}{2^{-27}} = \frac{2^{4 \cdot (-6)}}{2^{-27}} = \frac{2^{-24}}{2^{-27}} = 2^{-24 - (-27)} = 2^{-24+27} = 2^3 = 8 \)
\( 3^{-8} \cdot (3^6)^2 = 3^{-8} \cdot 3^{6 \cdot 2} = 3^{-8} \cdot 3^{12} = 3^{-8+12} = 3^4 = 81 \)
\( \frac{4^8 \cdot 11^{10}}{44^8} = \frac{4^8 \cdot 11^{10}}{(4 \cdot 11)^8} = \frac{4^8 \cdot 11^{10}}{4^8 \cdot 11^8} = 4^{8-8} \cdot 11^{10-8} = 4^0 \cdot 11^2 = 1 \cdot 121 = 121 \)