Solve (1)0.027^frac{1{3}}-(-1/7)^-2+(27/9)^frac{1{2}}-(sqrt{2}-1)^0

$$( 1 ) 0.027 ^ { \frac { 1 } { 3 } } - ( - \frac { 1 } { 7 } ) ^ { - 2 } + ( 2 \frac { 7 } { 9 } ) ^ { \frac { 1 } { 2 } } - ( \sqrt { 2 } - 1 ) ^ { 0 }$$

Evaluate

$$-\frac{1441}{30}\approx -48.033333333$$

Solution Steps

Calculate 0.027 to the power of \frac{1}{3} and get \frac{3}{10}.

$$1\times \frac{3}{10}-\left(-\frac{1}{7}\right)^{-2}+\left(\frac{2\times 9+7}{9}\right)^{\frac{1}{2}}-\left(\sqrt{2}-1\right)^{0}$$

Multiply 1 and \frac{3}{10} to get \frac{3}{10}.

$$\frac{3}{10}-\left(-\frac{1}{7}\right)^{-2}+\left(\frac{2\times 9+7}{9}\right)^{\frac{1}{2}}-\left(\sqrt{2}-1\right)^{0}$$

Calculate -\frac{1}{7} to the power of -2 and get 49.

$$\frac{3}{10}-49+\left(\frac{2\times 9+7}{9}\right)^{\frac{1}{2}}-\left(\sqrt{2}-1\right)^{0}$$

Subtract 49 from \frac{3}{10} to get -\frac{487}{10}.

$$-\frac{487}{10}+\left(\frac{2\times 9+7}{9}\right)^{\frac{1}{2}}-\left(\sqrt{2}-1\right)^{0}$$

Multiply 2 and 9 to get 18.

$$-\frac{487}{10}+\left(\frac{18+7}{9}\right)^{\frac{1}{2}}-\left(\sqrt{2}-1\right)^{0}$$

Add 18 and 7 to get 25.

$$-\frac{487}{10}+\left(\frac{25}{9}\right)^{\frac{1}{2}}-\left(\sqrt{2}-1\right)^{0}$$

Calculate \frac{25}{9} to the power of \frac{1}{2} and get \frac{5}{3}.

$$-\frac{487}{10}+\frac{5}{3}-\left(\sqrt{2}-1\right)^{0}$$

Add -\frac{487}{10} and \frac{5}{3} to get -\frac{1411}{30}.

$$-\frac{1411}{30}-\left(\sqrt{2}-1\right)^{0}$$

Calculate \sqrt{2}-1 to the power of 0 and get 1.

$$-\frac{1411}{30}-1$$

Subtract 1 from -\frac{1411}{30} to get -\frac{1441}{30}.

$$-\frac{1441}{30}$$

Factor

$$-\frac{1441}{30} = -48\frac{1}{30} = -48.03333333333333$$