Question

1. (1/16) в -0,75 +810000в 0,25 - (7 19/32) в 1/5 = 2. 27 в 2/3 - (-2)_ в -2+ (3 3/8) в -1/3 = 3.(0,001) в -1/3 - 2 в -2* 64 в2\3- 8 в -1 1/3 = 4. (-0,5) в -4 - 625 в 0,25 - (2 1/4) в -1 1/2 =

Answer 1

$(1/16)^{-0,75} +810000^{0,25} - (7 \frac{19}{32}) ^{1/5}= \\ = (1/16)^{-3/4} +810000^{1/4} - ( \frac{243}{32}) ^{1/5}= \\ =16^{3/4} +81^{1/4}*10000^{1/4} - \frac{ \sqrt[5]{243}}{ \sqrt[5]{32}}= \\ = (\sqrt[4]{16} )^{3} + \sqrt[4]{81} * \sqrt[4]{10000} - \frac{ \sqrt[5]{243}}{ \sqrt[5]{32}}=2^3+3*10- \frac{3}{2} = \\ 8+30-1,5=36,5$

$27^{2/3} - (-2)^{-2}+ (3 \frac{3}{8} )^{-1/3} =27^{2/3} - ( \frac{1}{2} )^{2}+ (\frac{27}{8} )^{-1/3} = \\ = (\sqrt[3]{27} )^2- \frac{1}{4} + \frac{ \sqrt[3]{8} }{ \sqrt[3]{27} } =9-\frac{1}{4} +\frac{2}{3} =9-\frac{3}{12} +\frac{8}{12} =9+\frac{5}{12}=9 \frac{5}{12}$

$(0,001) ^{ -1/3} - 2^{-2}* 64 ^{2/3}- 8^{ -1 \frac{1}{3}} =\\=( \frac{1}{0,001} ) ^{1/3} - ( \frac{1}{2} )^{2}* ( \sqrt[3]{64}) ^2- 8^{ - \frac{4}{3}} =\\= \sqrt[3]{1000} - \frac{1}{4}*4^2-( \frac{1}{8} ) ^{ \frac{4}{3}} =10-4-( \frac{1}{ \sqrt[3]{8} } ) ^4=6-( \frac{1}{ 2 } ) ^4=6- \frac{1}{16} =5 \frac{15}{16}$

$(-0,5) ^{-4} - 625 ^{0,25} - (2 \frac{1}{4} )^{ -1 \frac{1}{2} } =(- \frac{1}{2} ) ^{-4} - 625 ^{ \frac{1}{4} } - ( \frac{9}{4} )^{ -\frac{3}{2} } = \\ = (-2)^4- \sqrt[4]{625} } - ( \frac{4}{9} )^{ \frac{3}{2} } =16 - 5 - ( \frac{ \sqrt{4} }{ \sqrt{9} } )^{ 3 }=11 - ( \frac{ 2 }{3 } )^{ 3 }=11- \frac{8}{27} = \\ =10 \frac{19}{27}$