Question

Encontre a forma simplificada para item:
a) 81⁰,⁷⁵
b) 2³,⁵ =
c) 16¹,²⁵ =​

Answer 1

Oie, tudo bom?

a)

$= 8 1{}^{0,75} \\ = (3 {}^{4} ) {}^{ \frac{75}{100} } \\ = (3 {}^{4} ) {}^{ \frac{3}{4} } \\ = 3 {}^{3} \\ \boxed{ = 27}$

b)

$= 2 {}^{3,5} \\ = 2 {}^{ \frac{35}{10} } \\ = 2 {}^{ \frac{7}{2} } \\ = \sqrt{2 {}^{7} } \\ = \sqrt{2 {}^{6 + 1} } \\ = \sqrt{2 {}^{6} \: . \: 2 {}^{1} } \\ = \sqrt{2 {}^{6} \: . \: 2 } \\ = \sqrt{2 {}^{6} } \sqrt{2} \\ = 2 {}^{3} \sqrt{2} \\ = 8 \sqrt{2} \\ \boxed{ ≈11,31}$

c)

$= 16 {}^{1,25} \\ = (2 {}^{4} ) {}^{ \frac{125}{100} } \\ = (2 {}^{4} ) {}^{ \frac{5}{4} } \\ = 2 {}^{5} \\ \boxed{ = 32}$

Att. NLE Top Shotta

Answer 2

Explicação passo-a-passo:

$a)(81) {}^{0.75} = (3 {}^{4} ) {}^{ \frac{75}{100} } = (3) {}^{ \frac{300}{100} } = 3 {}^{3} = 27$

$b) \: \: (2) {}^{3.5} = (2) {}^{ \frac{35}{10} } = (2) {}^{ \frac{7}{2} } = \sqrt[2]{2 {}^{7} } = \sqrt[2]{2 {}^{6} .2} = 2 {}^{3} . \sqrt[2]{2} = 8 \sqrt[2]{2}$

$c) \: \: (16) {}^{1.25} = (2 {}^{4} ) \frac{125}{100} = (2) \frac{500}{100} = 2 {}^{5} = 32$