Question

quanto é $(\frac{a}{b} \sqrt{a})^{3}$ ? urgente

Answer 1

Resposta:

$\frac{a^{4}}{b^{3}}.\sqrt{a}$

Explicação passo-a-passo:

$(\frac{a}{b} \sqrt{a})^{3}=(\frac{a}{b} .a^{\frac{1}{2} } )^{3}=(\frac{a^{(1+\frac{1}{2} }) }{b} )^{3}=(\frac{a^{\frac{3}{2} }}{b} )^{3}=\frac{a^{\frac{9}{2} }}{b^{3}} =\frac{a^{(\frac{8}{2}+\frac{1}{2})  }}{b^{3}} =\frac{a^4.a^{\frac{1}{2} }}{b^{3}} =\frac{a^{4}}{b^{3}}.\sqrt{a}$

Propriedades:

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