Resolver frac{sqrt[5]{64^9*128^3}*(sqrt[3]{724div27})}{sqrt[5]{32*243}}

$$\frac { \sqrt[ 5 ] { 64 ^ { 9 } \cdot 128 ^ { 3 } } \cdot ( \sqrt[ 3 ] { 724 \div 27 } ) } { \sqrt[ 5 ] { 32 \cdot 243 } }$$

Avaliar

$$\frac{16384\sqrt[3]{724}}{9}\approx 16346,456330386$$

Passos Para a Resolução

Calcule 64 elevado a 9 e obtenha 18014398509481984.

$$\frac{\sqrt[5]{18014398509481984\times 128^{3}}\sqrt[3]{\frac{724}{27}}}{\sqrt[5]{32\times 243}}$$

Calcule 128 elevado a 3 e obtenha 2097152.

$$\frac{\sqrt[5]{18014398509481984\times 2097152}\sqrt[3]{\frac{724}{27}}}{\sqrt[5]{32\times 243}}$$

Multiplique 18014398509481984 e 2097152 para obter 37778931862957161709568.

$$\frac{\sqrt[5]{37778931862957161709568}\sqrt[3]{\frac{724}{27}}}{\sqrt[5]{32\times 243}}$$

Calcule \sqrt[5]{37778931862957161709568} e obtenha 32768.

$$\frac{32768\sqrt[3]{\frac{724}{27}}}{\sqrt[5]{32\times 243}}$$

Multiplique 32 e 243 para obter 7776.

$$\frac{32768\sqrt[3]{\frac{724}{27}}}{\sqrt[5]{7776}}$$

Calcule \sqrt[5]{7776} e obtenha 6.

$$\frac{32768\sqrt[3]{\frac{724}{27}}}{6}$$

Dividir 32768\sqrt[3]{\frac{724}{27}} por 6 para obter \frac{16384}{3}\sqrt[3]{\frac{724}{27}}.

$$\frac{16384}{3}\sqrt[3]{\frac{724}{27}}$$