Question

transforme em uma potência de x a expressão:​

Answer 1

Boa tarde!

$\sqrt{x \sqrt{ x\sqrt{x} } } = (x(x({x}^{ \frac{1}{2} }))^{ \frac{1}{2} })^{ \frac{1}{2} } = {x}^{ \frac{1}{2} }. {x}^{ \frac{1}{4} }. {x}^{ \frac{1}{8} } = {x}^{ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} } = {x}^{ \frac{4}{8} + \frac{2}{8} + \frac{1}{8} } = {x}^{ \frac{7}{8} }$

Espero ter ajudado!

Answer 2

Resposta:

$x^{\frac{7}{8}$

Explicação passo-a-passo:

$\sqrt{x\sqrt{x\sqrt{x}}} =\\\sqrt{x\sqrt{x.x^{\frac{1}{2}}}}=\\\sqrt{x\sqrt{x^{(1+\frac{1}{2})}}}=\\\sqrt{x\sqrt{x^{(\frac{2+1}{2})}}}=\\\sqrt{x\sqrt{x^{\frac{3}{2}}}}=\\\sqrt{x.{x^{(\frac{3}{2}.\frac{1}{2})}}}=\\\sqrt{x.{x^{\frac{3}{4}}}}=\\\sqrt{{x^{(1+\frac{3}{4})}}}=\\\sqrt{{x^{(\frac{4+3}{4})}}}=\\\sqrt{{x^{\frac{7}{4}}}}=\\{x^{\frac{7}{4}.\frac{1}{2}}}=\\x^{\frac{7}{8}$

Propriedades:

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