Solve {left(25/4right)}^{-1/2}+-1^3-{left(8/27right)}^-frac{2{3}}-{0.125}^-frac{1{3}}+{left(1/2right)}^-1-{left(-sqrt{2}right)}^0

$${ \left( \frac{ 25 }{ 4 } \right) }^{ - \frac{ 1 }{ 2 } } + { -1 }^{ 3 } - { \left( \frac{ 8 }{ 27 } \right) }^{ - \frac{ 2 }{ 3 } } - { 0.125 }^{ - \frac{ 1 }{ 3 } } + { \left( \frac{ 1 }{ 2 } \right) }^{ -1 } - { \left(- \sqrt{ 2 } \right) }^{ 0 }$$

Evaluate

$$-3.85$$

Solution Steps

Calculate \frac{25}{4} to the power of -\frac{1}{2} and get \frac{2}{5}.

$$\frac{2}{5}+\left(-1\right)^{3}-\left(\frac{8}{27}\right)^{-\frac{2}{3}}-0.125^{-\frac{1}{3}}+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{2}{5}-1-\left(\frac{8}{27}\right)^{-\frac{2}{3}}-0.125^{-\frac{1}{3}}+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

Subtract 1 from \frac{2}{5} to get -\frac{3}{5}.

$$-\frac{3}{5}-\left(\frac{8}{27}\right)^{-\frac{2}{3}}-0.125^{-\frac{1}{3}}+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

Calculate \frac{8}{27} to the power of -\frac{2}{3} and get \frac{9}{4}.

$$-\frac{3}{5}-\frac{9}{4}-0.125^{-\frac{1}{3}}+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

Subtract \frac{9}{4} from -\frac{3}{5} to get -\frac{57}{20}.

$$-\frac{57}{20}-0.125^{-\frac{1}{3}}+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

Calculate 0.125 to the power of -\frac{1}{3} and get 2.

$$-\frac{57}{20}-2+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

Subtract 2 from -\frac{57}{20} to get -\frac{97}{20}.

$$-\frac{97}{20}+\left(\frac{1}{2}\right)^{-1}-\left(-\sqrt{2}\right)^{0}$$

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

$$-\frac{97}{20}+2-\left(-\sqrt{2}\right)^{0}$$

Add -\frac{97}{20} and 2 to get -\frac{57}{20}.

$$-\frac{57}{20}-\left(-\sqrt{2}\right)^{0}$$

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

$$-\frac{57}{20}-1$$

Subtract 1 from -\frac{57}{20} to get -\frac{77}{20}.

$$-\frac{77}{20}$$

Factor

$$-3.85$$