Solve [1/10+(1/10)^9*(1/21)^7:(1/14*frac{1}{15})^7]

$$[ \frac { 1 } { 10 } + ( \frac { 1 } { 10 } ) ^ { 9 } \cdot ( \frac { 1 } { 21 } ) ^ { 7 } : ( \frac { 1 } { 14 } \cdot \frac { 1 } { 15 } ) ^ { 7 } ]$$

Evaluate

$$\frac{11}{100}=0.11$$

Solution Steps

Calculate \frac{1}{10} to the power of 9 and get \frac{1}{1000000000}.

$$\frac{1}{10}+\frac{\frac{1}{1000000000}\times \left(\frac{1}{21}\right)^{7}}{\left(\frac{1}{14}\times \frac{1}{15}\right)^{7}}$$

Calculate \frac{1}{21} to the power of 7 and get \frac{1}{1801088541}.

$$\frac{1}{10}+\frac{\frac{1}{1000000000}\times \frac{1}{1801088541}}{\left(\frac{1}{14}\times \frac{1}{15}\right)^{7}}$$

Multiply \frac{1}{1000000000} and \frac{1}{1801088541} to get \frac{1}{1801088541000000000}.

$$\frac{1}{10}+\frac{\frac{1}{1801088541000000000}}{\left(\frac{1}{14}\times \frac{1}{15}\right)^{7}}$$

Multiply \frac{1}{14} and \frac{1}{15} to get \frac{1}{210}.

$$\frac{1}{10}+\frac{\frac{1}{1801088541000000000}}{\left(\frac{1}{210}\right)^{7}}$$

Calculate \frac{1}{210} to the power of 7 and get \frac{1}{18010885410000000}.

$$\frac{1}{10}+\frac{\frac{1}{1801088541000000000}}{\frac{1}{18010885410000000}}$$

Divide \frac{1}{1801088541000000000} by \frac{1}{18010885410000000} by multiplying \frac{1}{1801088541000000000} by the reciprocal of \frac{1}{18010885410000000}.

$$\frac{1}{10}+\frac{1}{1801088541000000000}\times 18010885410000000$$

Multiply \frac{1}{1801088541000000000} and 18010885410000000 to get \frac{1}{100}.

$$\frac{1}{10}+\frac{1}{100}$$

Add \frac{1}{10} and \frac{1}{100} to get \frac{11}{100}.

$$\frac{11}{100}$$

Factor

$$\frac{11}{2 ^ {2} \cdot 5 ^ {2}} = 0.11$$