Question

1 - encontre o valor de x

$x = ( {3}^{4} )^{ \frac{1}{2} } - \sqrt[7]{128} - {256}^{ \frac{1}{2} }$
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Answer 1

$x = ({3}^{4} )^{ \frac{1}{2}} - \sqrt[7]{128} - {256}^{ \frac{1}{2}}\\x = 3^{\frac{4}{2}} - \sqrt[7]{2^7} - (2^8)^{\frac{1}{2}} \\x = 3^2 - 2^{\frac{7}{7}} - 2^{\frac{8}{2}}\\x = 3^2 - 2^1 - 2^4\\x = 9 - 2 - 16\\x = -9$

Answer 2

Resposta:

x= -9

Explicação passo-a-passo:

Fatore os números:

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 | 1  /  2 . 2 . 2 . 2 . 2 . 2 . 2 = 2^7= 128

256 | 2

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 | 1  / 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 = 2^8= 256

Resolvendo:

$x = ({3}^{4})^{\frac{1}{2}}-\sqrt[7]{128}-{256}^{\frac{1}{2}}\\x = {3}^{4.\frac{1}{2}}-\sqrt[7]{2^{7}}-{2}^{8.\frac{1}{2}}\\x = {3}^{2} -2^{\frac{7}{7}}-{2}^{4}\\x = 9-2-16\\x=-9$

Propriedades:

$(a^{m})^{n}=a^{m.n}\\\\\sqrt[n]{x^m} =x^{\frac{m}{n} }\\\\a^{m}a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \\\\a^{0}=1\\\\a^{1}=a$