Solve (-5)^2-3^2+(2/8)^0/3^-2+frac{1{5}+1/2}

$$\frac { ( - 5 ) ^ { 2 } - 3 ^ { 2 } + ( \frac { 2 } { 8 } ) ^ { 0 } } { 3 ^ { - 2 } + \frac { 1 } { 5 } + \frac { 1 } { 2 } }$$

Evaluate

$$\frac{1530}{73}\approx 20.95890411$$

Solution Steps

Calculate -5 to the power of 2 and get 25.

$$\frac{25-3^{2}+\left(\frac{2}{8}\right)^{0}}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{25-9+\left(\frac{2}{8}\right)^{0}}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Subtract 9 from 25 to get 16.

$$\frac{16+\left(\frac{2}{8}\right)^{0}}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{16+\left(\frac{1}{4}\right)^{0}}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Calculate \frac{1}{4} to the power of 0 and get 1.

$$\frac{16+1}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Add 16 and 1 to get 17.

$$\frac{17}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

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

$$\frac{17}{\frac{1}{9}+\frac{1}{5}+\frac{1}{2}}$$

Add \frac{1}{9} and \frac{1}{5} to get \frac{14}{45}.

$$\frac{17}{\frac{14}{45}+\frac{1}{2}}$$

Add \frac{14}{45} and \frac{1}{2} to get \frac{73}{90}.

$$\frac{17}{\frac{73}{90}}$$

Divide 17 by \frac{73}{90} by multiplying 17 by the reciprocal of \frac{73}{90}.

$$17\times \frac{90}{73}$$

Multiply 17 and \frac{90}{73} to get \frac{1530}{73}.

$$\frac{1530}{73}$$

Factor

$$\frac{2 \cdot 3 ^ {2} \cdot 5 \cdot 17}{73} = 20\frac{70}{73} = 20.958904109589042$$