Solve {left(31/3right)}^2--6.54/13+-2^4/-2^3+4

$${ \left(3 \frac{ 1 }{ 3 } \right) }^{ 2 } --6.5 \frac{ 4 }{ 13 } + \frac{ { -2 }^{ 4 } }{ { -2 }^{ 3 } +4 }$$

Evaluate

$$\frac{3257}{234}\approx 13.918803419$$

Solution Steps

Multiply 3 and 3 to get 9.

$$\left(\frac{9+1}{3}\right)^{2}-\left(-\frac{6.5\times 13+4}{13}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Add 9 and 1 to get 10.

$$\left(\frac{10}{3}\right)^{2}-\left(-\frac{6.5\times 13+4}{13}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Calculate \frac{10}{3} to the power of 2 and get \frac{100}{9}.

$$\frac{100}{9}-\left(-\frac{6.5\times 13+4}{13}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Multiply 6.5 and 13 to get 84.5.

$$\frac{100}{9}-\left(-\frac{84.5+4}{13}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Add 84.5 and 4 to get 88.5.

$$\frac{100}{9}-\left(-\frac{88.5}{13}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Expand \frac{88.5}{13} by multiplying both numerator and the denominator by 10.

$$\frac{100}{9}-\left(-\frac{885}{130}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Reduce the fraction \frac{885}{130} to lowest terms by extracting and canceling out 5.

$$\frac{100}{9}-\left(-\frac{177}{26}\right)+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

The opposite of -\frac{177}{26} is \frac{177}{26}.

$$\frac{100}{9}+\frac{177}{26}+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Add \frac{100}{9} and \frac{177}{26} to get \frac{4193}{234}.

$$\frac{4193}{234}+\frac{\left(-2\right)^{4}}{\left(-2\right)^{3}+4}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{4193}{234}+\frac{16}{\left(-2\right)^{3}+4}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{4193}{234}+\frac{16}{-8+4}$$

Add -8 and 4 to get -4.

$$\frac{4193}{234}+\frac{16}{-4}$$

Divide 16 by -4 to get -4.

$$\frac{4193}{234}-4$$

Subtract 4 from \frac{4193}{234} to get \frac{3257}{234}.

$$\frac{3257}{234}$$

Factor

$$\frac{3257}{2 \cdot 13 \cdot 3 ^ {2}} = 13\frac{215}{234} = 13.918803418803419$$