Question

Допоможіть будь ласка!

Answer 1

Ответ:

1) B) 33

2) Д) 54

3) A) 19

Объяснение:

1)

$a^{-3} :a^{-1} +8a^{-1} =a^{-3-(-1)} +8a^{-1} =a^{-2} +8a^{-1} =a^{-1}(a^{-1}+8)=\frac{1}{a^{1} } (\frac{1}{a^{1} }+8)=\\\\\frac{1}{a} (\frac{1}{a} +8)$

$a=\frac{1}{3} \\\\\frac{1}{a} =1:\frac{1}{3} =1*\frac{3}{1} =3\\\\\frac{1}{a}(\frac{1}{a} +8)=3(3+8)=3*11=33$

2)

$2(a^{2} )^{-1} *a^{-1} =2*a^{2*(-1)} *a^{-1}=2*a^{-2} *a^{-1}=2*a^{-2+(-1)}=2*a^{-2-1}=\\\\2*a^{-3}=2*\frac{1}{a^{3}} =\frac{2}{a^{3} }$

$a=\frac{1}{3} \\\\a^{3}= (\frac{1}{3})^{3} =\frac{1^{3} }{3^{3} } =\frac{1}{27}\\\\\frac{2}{a^{3} }=2:\frac{1}{27} =2*\frac{27}{1} =2*27=54$

3)

$a^{3} *a^{-4} +16a^{0} =a^{3+(-4)} +16a^{0} =a^{-1} +16a^{0} =\frac{1} {a^{1}} +16*1=\frac{1}{a} +16$

$a=\frac{1}{3} \\\\\frac{1}{a} =1:\frac{1}{3} =1*\frac{3}{1} =3\\\\\frac{1}{a} +16=3+16=19$