Question

Вычислите 25^1,5+(0,25)^-0,5 -81^0,75

Answer 1

$25^{1,5}+0,25^{-0,5}-81^{0,75}=(5^{2})^{1,5}+(2^{-2})^{-0,5}-(3^{4})^{0,75}= \\ 5^{3}+2-3^{3}=125+2-27=100$

Answer 2

$25 ^{1.5} +(0.25) ^{-0.5} -81 ^{0.75} =100 \\ \\ 1)25 ^{1.5} =(5 ^{2}) ^{1.5} =5 ^{2*1.5} =5 ^{3} =125 \\ 2)(0.25) ^{-0.5} =(0.5 ^{2} ) ^{-0.5} =( (\frac{5}{10} ) ^{2}) ^{-0.5} =( (\frac{1}{2} ) ^{2}) ^{-0.5} = ( 2 ^{2}) ^{0.5} =\\ =2 ^{1} =2\\3)81 ^{0.75} =(3 ^{4} ) ^{0.75} =3 ^{4*0.75} =3 ^{3} =27\\4) 125+2=127\\5)127-27=100$