Question

Решите срочно пожалуйста!!!!!

Answer 1

$displaystyle tt 1.\\a). 2^{-3}cdot2^{-2}=2^{-5}=frac{1}{2^{5}}=frac{1}{32};\\b). bigg(frac{1}{8}bigg)^{-10}:bigg(frac{1}{8}bigg)^{-8}=8^{10}:8^{8}=8^{2}=64;\\c). (3^{-4})^{5}cdot3^{16}=3^{-20}cdot3^{16}=3^{-4}=frac{1}{81};\\d). bigg(1frac{1}{9}bigg)^{-2}=bigg(frac{10}{9}bigg)^{-2}=bigg(frac{9}{10}bigg)^{2}=0,81;$

$displaystyle tt 2.\\a). 16^{-3}cdot8^{4}=(2^{4})^{-3}cdot(2^{3})^{4}=2^{-12}cdot2^{12}=2^{0}=1;\\b). (31^{-3})^{7}:31^{-20}=31^{-21}cdot31^{20}=31^{-1}=frac{1}{31};\\c). 81^{5}cdot9^{-11}:3^{-4}=(3^{4})^{5}cdot(3^{2})^{-11}cdot3^{4}=3^{20}cdot3^{-22}cdot3^{4}=3^{2}=9;\\d). 125^{-7}:(5^{0}cdot25^{-11})=(5^{3})^{-7}cdot(5^{2})^{11}=5^{-21}cdot5^{22}=5;$

$displaystyle tt 3. (6^{3-n})^{4}cdot6^{2n-8}cdot36=6^{12-4n}cdot6^{2n-8}cdot6^{2}=6^{6-2n};\\\4.\\a). frac{15x^{-6}}{y^{-5}}cdotfrac{y^{-2}}{25x^{3}}=15x^{-6}cdot y^{5}cdot y^{-2}:25x^{3}=0,6x^{-9}y^{3};$

$displaystyle tt b). bigg(frac{9}{a^{8}b^{-5}}bigg)^{-4}cdotbigg(frac{a^{4}b^{-6}}{27}bigg)^{-3}=frac{a^{32}b^{-20}}{3^{8}}cdotfrac{3^{9}}{a^{12}b^{-18}}=3a^{20}b^{-2};$