Question

determine o radical correspondente a cada potência
$a\\ 81 \times \frac{1}{4}$
$b\\ 16 \times \frac{1}{2}$
$c \\ 10000 \times \frac{3}{4}$
$d \\ 27 \times \frac{2}{3}$


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Answer 1

a)

${81}^{ \frac{1}{4} } = \sqrt[4]{81} = \sqrt[4]{ {3}^{4} } = 3$

b)

${16}^{ \frac{1}{2} } = \sqrt{16} = 4$

c)

${10000}^{ \frac{3}{4} } = \sqrt[4]{ {10000}^{3} } = \sqrt[4]{ {10}^{12} } = 1000$

d)

${27}^{ \frac{2}{3} } = \sqrt[3]{2 {7}^{2} } = \sqrt[3]{ {( {3}^{3}) }^{2} } = \sqrt[3]{ {3}^{6} } = 9$

Answer 2

Explicação passo-a-passo:

Lembre-se que:

$\sf a^{\frac{b}{c}}=\sqrt[c]{a^b}$

Assim:

a)

$\sf 81^{\frac{1}{4}}=\red{\sqrt[4]{81}}$

$\sf 81^{\frac{1}{4}}=\sqrt[4]{3^4}$

$\sf 81^{\frac{1}{4}}=3$

b)

$\sf 16^{\frac{1}{2}}=\red{\sqrt[2]{16}}$

$\sf 16^{\frac{1}{2}}=\sqrt{4^2}$

$\sf 16^{\frac{1}{2}}=4$

c)

$\sf 10000^{\frac{3}{4}}=\red{\sqrt[4]{10000^3}}$

$\sf 10000^{\frac{3}{4}}=\sqrt[4]{(10^4)^3}$

$\sf 10000^{\frac{3}{4}}=\sqrt[4]{(10^3)^4}$

$\sf 10000^{\frac{3}{4}}=10^3$

$\sf 10000^{\frac{3}{4}}=1000$

d)

$\sf 27^{\frac{2}{3}}=\red{\sqrt[3]{27^2}}$

$\sf 27^{\frac{2}{3}}=\sqrt[3]{(3^3)^2}$

$\sf 27^{\frac{2}{3}}=\sqrt[3]{(3^2)^3}$

$\sf 27^{\frac{2}{3}}=3^2$

$\sf 27^{\frac{2}{3}}=9$