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

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

Evaluate

$$-\frac{491}{225}\approx -2.182222222$$

Solution Steps

Divide 2 by 2 to get 1.

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

Calculate \frac{4}{9} to the power of 1 and get \frac{4}{9}.

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

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

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

Subtract 3 from \frac{4}{9} to get -\frac{23}{9}.

$$-\frac{23}{9}+\left(\frac{1}{5}\right)^{2}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

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

$$-\frac{23}{9}+\frac{1}{25}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

Add -\frac{23}{9} and \frac{1}{25} to get -\frac{566}{225}.

$$-\frac{566}{225}+\sqrt[3]{-\frac{8}{27}}+\left(\frac{3}{5}\right)^{0}$$

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

$$-\frac{566}{225}-\frac{2}{3}+\left(\frac{3}{5}\right)^{0}$$

Subtract \frac{2}{3} from -\frac{566}{225} to get -\frac{716}{225}.

$$-\frac{716}{225}+\left(\frac{3}{5}\right)^{0}$$

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

$$-\frac{716}{225}+1$$

Add -\frac{716}{225} and 1 to get -\frac{491}{225}.

$$-\frac{491}{225}$$

Factor

$$-\frac{491}{225} = -2\frac{41}{225} \approx -2.182222222$$