Question

Вычислить.Даю 99 баллов.

Answer 1

$(a^x)^y=a^{x*y} \\ a^{-x}= \frac{1}{a^x}$

$1) 81=3^4~~~~32=2^5 ~~~~~8=2^3~~~~27=3^3~~~~~256=2^8 \\ \\ ~81^{0.75}*32^{-0.4}-8^{- \frac{2}{3} }*27^{ \frac{1}{3} }+256^{0.5}= \\ = (3^{4})^{0.75}*(2^5)^{-0.4}-(2^3)^{- \frac{2}{3} }*(3^3)^{ \frac{1}{3} }+(2^8)^{0.5}= \\ 3^{4*0.75}*2^{5*(-0.4)}-2^{3*(- \frac{2}{3} )}*3^{3*\frac{1}{3}}+2^{8*0.5}=3^3*2^{-2}-2^{-2}*3^1+2^4= \\ =3^3* \frac{1}{2^2}- \frac{1}{2^2}*3^1+2^4=27* \frac{1}{4} -\frac{1}{4}*3+16=6,75-0,75+16=22 \\ \\ 81^{0.75}*32^{-0.4}-8^{- \frac{2}{3} }*27^{ \frac{1}{3} }+256^{0.5}=22$


$2)~ \sqrt{ \frac{9}{16} \sqrt{ \frac{33^2-25^2}{29} } } =2)~ \sqrt{ \frac{9}{16} \sqrt{ \frac{(33-25)(33+25)}{29} } } = \sqrt{ \frac{9}{16} \sqrt{ \frac{8*58}{29} } } = \\ =\sqrt{ \frac{9}{16} \sqrt{ \frac{8*2*29}{29} } } =\sqrt{ \frac{9}{16} \sqrt{ 8*2 } } =\sqrt{ \frac{9}{16} \sqrt{ 16 } } =\sqrt{ \frac{9}{16}*4 } =\sqrt{ \frac{9}{4} } = \\ =\frac{ \sqrt{9} }{ \sqrt{4} } = \frac{3}{2} =1 \frac{1}{2} =1.5$

Answer 2

$1)...=(3^4) ^{0,75} *(2^5) ^{-0,4} -(2^3) ^{-2/3}*(3^3) ^{1/3} +(2^8) ^{0,5} =$$3^3*2 ^{-2} -2 ^{-2} *3+2^4=27/4-3/4+16=6+16=22$
$2)...=3/4* \sqrt[4]{(33-25)(33+25)/29} =3/4* \sqrt[4]{8*58/29} =3/4* \sqrt[4]{16}$$=3/4*2=3/2=1,5$