Question

alguém pode responder estas questão aqui pra mim gente por favor

Answer 1

6.a)
$\sqrt{1.69} = \sqrt{ \frac{169}{100} } = \frac{ \sqrt{169} }{ \sqrt{100} } \\ \frac{ \sqrt{13 {}^{2} } }{ \sqrt{10 {}^{2} } } = \frac{13}{10}$
6.b)
${}^{3} \sqrt - { \frac{216}{125} } = - \frac{ {}^{3} \sqrt{216} }{ {}^{3} \sqrt{125} } = \\ - \frac{ {}^{3} \sqrt{6 {}^{2} } }{ {}^{3} \sqrt{5 {}^{3} } } = - \frac{6}{5}$
6.c)
$\frac{ {}^{4} \sqrt{81} }{ {}^{4} \sqrt{625} } = \frac{ {}^{4} \sqrt{3 {}^{4} } }{ {}^{4} \sqrt{5 {}^{4} } } = \frac{3}{5}$
6.d)
${ }^{3} \sqrt{ - \frac{2197}{1000} } = - {}^{3} \sqrt{ \frac{2197}{1000} } = \\ - \frac{ {}^{3} \sqrt{2197} }{ {}^{3} \sqrt{1000} } = - \frac{ {}^{3} \sqrt{13 {}^{3} } }{ {}^{3} \sqrt{10 {}^{3} } } = \\ - \frac{13}{10}$
7.a)
$121 {}^{0.9} \div 121 {}^{0.4} = \\ 121 {}^{0.5} = (11 {}^{2} ) {}^{0.5} = \\ (11 {}^{2} ) {}^{ \frac{1}{2} } = 11 {}^{2 \times } {}^{ \frac{1}{2} } = 11 {}^{1} = 11$
7.b)
$0.3 {}^{8} \times 0.3 {}^{ - 7} \times 0.3 {}^{ 2} \\ 0.3 {}^{8 - 7 + 2} = 0.3 {}^{3} \\ (\frac{3}{10} ) {}^{3} = \frac{3 {}^{3} }{10 {}^{3} } \\ \frac{27}{1000} = 0.027$
7.c)
$\frac{( - 3) {}^{ \frac{1}{3} } }{( - 3) {}^{ - 1} } = ( - 3) {}^{ \frac{1}{3} } \times ( - 3) = \\ - 3 \times ( - 3) {}^{ \frac{1}{2} } = \\ - 3 \times {}^{3} \sqrt{ - 3 {}^{ {}^{ - 1} } } = \\ - 3 \times {}^{3} \sqrt{ - 3}$
7.d)
$( - 32) {}^{ \frac{5}{2} } {}^{ \times \frac{ 4}{25} } = ( - 32) {}^{5 \times \frac{2}{25} } = \\ (- 32) {}^{ \frac{2}{5} } = {}^{5} \sqrt{ - 32 {}^{2} } = \\ {}^{5} \sqrt{32} {}^{2} = {}^{5} \sqrt{2 {}^{5} } {}^{2} \\ 2 {}^{2} = 4$