Solve (-1/3)^{2}-0,17+3,2*10^11/1,6*10^12*[(7/9)^13]^0*frac{1/5}{1-frac{4}{5}}=

$$( - \frac { 1 } { 3 } ) ^ { 2 } - 0,17 + \frac { 3,2 \cdot 10 ^ { 11 } } { 1,6 \cdot 10 ^ { 12 } } \cdot [ ( \frac { 7 } { 9 } ) ^ { 13 } ] ^ { 0 } \cdot \frac { \frac { 1 } { 5 } } { 1 - \frac { 4 } { 5 } } =$$

Evaluate

$$\frac{127}{900}\approx 0,141111111$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 13 and 0 to get 0.

$$\left(-\frac{1}{3}\right)^{2}-0,17+\frac{3,2\times 10^{11}}{1,6\times 10^{12}}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

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

$$\frac{1}{9}-0,17+\frac{3,2\times 10^{11}}{1,6\times 10^{12}}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Subtract 0,17 from \frac{1}{9} to get -\frac{53}{900}.

$$-\frac{53}{900}+\frac{3,2\times 10^{11}}{1,6\times 10^{12}}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Cancel out 10^{11} in both numerator and denominator.

$$-\frac{53}{900}+\frac{3,2}{1,6\times 10}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Multiply 1,6 and 10 to get 16.

$$-\frac{53}{900}+\frac{3,2}{16}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Expand \frac{3,2}{16} by multiplying both numerator and the denominator by 10.

$$-\frac{53}{900}+\frac{32}{160}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Reduce the fraction \frac{32}{160} to lowest terms by extracting and canceling out 32.

$$-\frac{53}{900}+\frac{1}{5}\times \left(\frac{7}{9}\right)^{0}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Calculate \frac{7}{9} to the power of 0 and get 1.

$$-\frac{53}{900}+\frac{1}{5}\times 1\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Multiply \frac{1}{5} and 1 to get \frac{1}{5}.

$$-\frac{53}{900}+\frac{1}{5}\times \frac{\frac{1}{5}}{1-\frac{4}{5}}$$

Subtract \frac{4}{5} from 1 to get \frac{1}{5}.

$$-\frac{53}{900}+\frac{1}{5}\times \frac{\frac{1}{5}}{\frac{1}{5}}$$

Divide \frac{1}{5} by \frac{1}{5} to get 1.

$$-\frac{53}{900}+\frac{1}{5}\times 1$$

Multiply \frac{1}{5} and 1 to get \frac{1}{5}.

$$-\frac{53}{900}+\frac{1}{5}$$

Add -\frac{53}{900} and \frac{1}{5} to get \frac{127}{900}.

$$\frac{127}{900}$$

Factor

$$\frac{127}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2}} = 0.1411111111111111$$