Resolver (4/9)^-2+sqrt[3]{-27}+(1/5)^2+sqrt[3]{-8/27}+(3/5)^0

$$( \frac { 4 } { 9 } ) ^ { - 2 } + \sqrt[ 3 ] { - 27 } + ( \frac { 1 } { 5 } ) ^ { 2 } + \sqrt[ 3 ] { - \frac { 8 } { 27 } } + ( \frac { 3 } { 5 } ) ^ { 0 }$$

Avaliar

$$\frac{2923}{1200}\approx 2,435833333$$

Passos Para a Resolução

Calcule \frac{4}{9} elevado a -2 e obtenha \frac{81}{16}.

$$\frac{81}{16}+\sqrt[3]{-27}+\left(\frac{1}{5}\right)^{2}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

Calcule \sqrt[3]{-27} e obtenha -3.

$$\frac{81}{16}-3+\left(\frac{1}{5}\right)^{2}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

Subtraia 3 de \frac{81}{16} para obter \frac{33}{16}.

$$\frac{33}{16}+\left(\frac{1}{5}\right)^{2}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

Calcule \frac{1}{5} elevado a 2 e obtenha \frac{1}{25}.

$$\frac{33}{16}+\frac{1}{25}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

Some \frac{33}{16} e \frac{1}{25} para obter \frac{841}{400}.

$$\frac{841}{400}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

Calcule \sqrt[3]{-\frac{8}{27}} e obtenha -\frac{2}{3}.

$$\frac{841}{400}-\frac{2}{3}+\left(\frac{3}{5}\right)^{0}$$

Subtraia \frac{2}{3} de \frac{841}{400} para obter \frac{1723}{1200}.

$$\frac{1723}{1200}+\left(\frac{3}{5}\right)^{0}$$

Calcule \frac{3}{5} elevado a 0 e obtenha 1.

$$\frac{1723}{1200}+1$$

Some \frac{1723}{1200} e 1 para obter \frac{2923}{1200}.

$$\frac{2923}{1200}$$

Fatorizar

$$\frac{37 \cdot 79}{2 ^ {4} \cdot 3 \cdot 5 ^ {2}} = 2\frac{523}{1200} = 2,4358333333333335$$