Solve 3^-2-3^-3*{left(2/3right)}^-3-13^0-1^3

$${ 3 }^{ -2 } - { 3 }^{ -3 } \times { \left( \frac{ 2 }{ 3 } \right) }^{ -3 } - { 13 }^{ 0 } - { 1 }^{ 3 }$$

Evaluate

$$-\frac{145}{72}\approx -2.013888889$$

Solution Steps

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

$$\frac{1}{9}-3^{-3}\times \left(\frac{2}{3}\right)^{-3}-13^{0}-1^{3}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{1}{9}-\frac{1}{27}\times \left(\frac{2}{3}\right)^{-3}-13^{0}-1^{3}$$

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

$$\frac{1}{9}-\frac{1}{27}\times \frac{27}{8}-13^{0}-1^{3}$$

Multiply \frac{1}{27} and \frac{27}{8} to get \frac{1}{8}.

$$\frac{1}{9}-\frac{1}{8}-13^{0}-1^{3}$$

Subtract \frac{1}{8} from \frac{1}{9} to get -\frac{1}{72}.

$$-\frac{1}{72}-13^{0}-1^{3}$$

Calculate 13 to the power of 0 and get 1.

$$-\frac{1}{72}-1-1^{3}$$

Subtract 1 from -\frac{1}{72} to get -\frac{73}{72}.

$$-\frac{73}{72}-1^{3}$$

Calculate 1 to the power of 3 and get 1.

$$-\frac{73}{72}-1$$

Subtract 1 from -\frac{73}{72} to get -\frac{145}{72}.

$$-\frac{145}{72}$$

Factor

$$-\frac{145}{72} = -2\frac{1}{72} = -2.013888888888889$$