Question

Efetue: ⁴√a⁵b² ÷ ⁴√ab , ab ≠ 5 cálculos

Answer 1

Explicação passo a passo:

⁴√a⁵b² ÷ ⁴√ab =

⁴√ ( a^5b² : a¹b¹ ) =

a^5 : a¹ = a^4 conserva a base e diminui expoentes

b² : b¹ = b¹ idem acima

resposta da divisão das bases = a^4b¹ >>>

reescrevendo

⁴√(a^4b¹) =elimina expoente 4

resposta >>>> a^4 * ⁴√b

Answer 2

Resposta:

$\sqrt[4]{a}^5b^2 : \sqrt[4]{ab}\\\\\mathrm{Aplicar\:a\:seguinte\:propriedade\:dos\:radicais:}\:\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:\quad \mathrm{assumindo\:que}\:a\ge 0,\:b\ge 0\\\\\sqrt[4]{ab}=\sqrt[4]{b}\sqrt[4]{a}\\\\=\frac{\left(\sqrt[4]{a}\right)^5b^2}{\sqrt[4]{b}\sqrt[4]{a}}\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:radicais}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\\\\\sqrt[4]{b}=b^{\frac{1}{4}}\\\\=\frac{\left(\sqrt[4]{a}\right)^5b^2}{b^{\frac{1}{4}}\sqrt[4]{a}}$

$=\frac{\left(\sqrt[4]{a}\right)^5b\sqrt[4]{b^3}}{\sqrt[4]{a}}\\\\=\left(\sqrt[4]{a}\right)^4b\sqrt[4]{b^3}\\\\=ab\sqrt[4]{b^3}$