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

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

Evaluate

$$-\frac{2970}{73}\approx -40.684931507$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

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

Calculate 3 to the power of 2 and get 9.

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

Subtract 9 from -25 to get -34.

$$\frac{-34+\left(\frac{2}{3}\right)^{0}}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Calculate \frac{2}{3} to the power of 0 and get 1.

$$\frac{-34+1}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

Add -34 and 1 to get -33.

$$\frac{-33}{3^{-2}+\frac{1}{5}+\frac{1}{2}}$$

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

$$\frac{-33}{\frac{1}{9}+\frac{1}{5}+\frac{1}{2}}$$

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

$$\frac{-33}{\frac{14}{45}+\frac{1}{2}}$$

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

$$\frac{-33}{\frac{73}{90}}$$

Divide -33 by \frac{73}{90} by multiplying -33 by the reciprocal of \frac{73}{90}.

$$-33\times \frac{90}{73}$$

Multiply -33 and \frac{90}{73} to get -\frac{2970}{73}.

$$-\frac{2970}{73}$$

Factor

$$-\frac{2970}{73} = -40\frac{50}{73} = -40.68493150684932$$