Solve 2^10/2^13+2^3div{left(5/13right)}^-15^-3/{2^-4}

$$\frac{ { 2 }^{ 10 } }{ { 2 }^{ 13 } } + { 2 }^{ 3 } \div { \left( \frac{ 5 }{ 13 } \right) }^{ -1 } \frac{ { 5 }^{ -3 } }{ { 2 }^{ -4 } }$$

Evaluate

$$\frac{1349}{2600}\approx 0.518846154$$

Solution Steps

Rewrite 2^{13} as 2^{10}\times 2^{3}. Cancel out 2^{10} in both numerator and denominator.

$$\frac{1}{2^{3}}+\frac{2^{3}}{\left(\frac{5}{13}\right)^{-1}}\times \frac{5^{-3}}{2^{-4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8}+\frac{2^{3}}{\left(\frac{5}{13}\right)^{-1}}\times \frac{5^{-3}}{2^{-4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8}+\frac{8}{\left(\frac{5}{13}\right)^{-1}}\times \frac{5^{-3}}{2^{-4}}$$

Calculate \frac{5}{13} to the power of -1 and get \frac{13}{5}.

$$\frac{1}{8}+\frac{8}{\frac{13}{5}}\times \frac{5^{-3}}{2^{-4}}$$

Divide 8 by \frac{13}{5} by multiplying 8 by the reciprocal of \frac{13}{5}.

$$\frac{1}{8}+8\times \frac{5}{13}\times \frac{5^{-3}}{2^{-4}}$$

Multiply 8 and \frac{5}{13} to get \frac{40}{13}.

$$\frac{1}{8}+\frac{40}{13}\times \frac{5^{-3}}{2^{-4}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{1}{8}+\frac{40}{13}\times \frac{\frac{1}{125}}{2^{-4}}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\frac{1}{8}+\frac{40}{13}\times \frac{\frac{1}{125}}{\frac{1}{16}}$$

Divide \frac{1}{125} by \frac{1}{16} by multiplying \frac{1}{125} by the reciprocal of \frac{1}{16}.

$$\frac{1}{8}+\frac{40}{13}\times \frac{1}{125}\times 16$$

Multiply \frac{1}{125} and 16 to get \frac{16}{125}.

$$\frac{1}{8}+\frac{40}{13}\times \frac{16}{125}$$

Multiply \frac{40}{13} and \frac{16}{125} to get \frac{128}{325}.

$$\frac{1}{8}+\frac{128}{325}$$

Add \frac{1}{8} and \frac{128}{325} to get \frac{1349}{2600}.

$$\frac{1349}{2600}$$

Factor

$$\frac{19 \cdot 71}{2 ^ {3} \cdot 5 ^ {2} \cdot 13} = 0.5188461538461538$$