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

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

Evaluate

$$\frac{2923}{1200}\approx 2.435833333$$

Solution Steps

Calculate \frac{4}{9} to the power of -2 and get \frac{81}{16}.

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

Calculate \sqrt[3]{-27} and get -3.

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

Subtract 3 from \frac{81}{16} to get \frac{33}{16}.

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

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

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

Add \frac{33}{16} and \frac{1}{25} to get \frac{841}{400}.

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

Calculate \sqrt[3]{-\frac{8}{27}} and get -\frac{2}{3}.

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

Subtract \frac{2}{3} from \frac{841}{400} to get \frac{1723}{1200}.

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

Calculate \frac{3}{5} to the power of 0 and get 1.

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

Add \frac{1723}{1200} and 1 to get \frac{2923}{1200}.

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

Factor

$$\frac{37 \cdot 79}{2 ^ {4} \cdot 3 \cdot 5 ^ {2}} = 2\frac{523}{1200} = 2.4358333333333335$$