Solve 5^{-2}+(-1)^4-(-2)^2+(-1/3)^-3+(-7)^0

$$5 ^ { - 2 } + ( - 1 ) ^ { 4 } - ( - 2 ) ^ { 2 } + ( - \frac { 1 } { 3 } ) ^ { - 3 } + ( - 7 ) ^ { 0 }$$

Evaluate

$$-\frac{724}{25}=-28.96$$

Solution Steps

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{1}{25}+\left(-1\right)^{4}-\left(-2\right)^{2}+\left(-\frac{1}{3}\right)^{-3}+\left(-7\right)^{0}$$

Calculate -1 to the power of 4 and get 1.

$$\frac{1}{25}+1-\left(-2\right)^{2}+\left(-\frac{1}{3}\right)^{-3}+\left(-7\right)^{0}$$

Add \frac{1}{25} and 1 to get \frac{26}{25}.

$$\frac{26}{25}-\left(-2\right)^{2}+\left(-\frac{1}{3}\right)^{-3}+\left(-7\right)^{0}$$

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

$$\frac{26}{25}-4+\left(-\frac{1}{3}\right)^{-3}+\left(-7\right)^{0}$$

Subtract 4 from \frac{26}{25} to get -\frac{74}{25}.

$$-\frac{74}{25}+\left(-\frac{1}{3}\right)^{-3}+\left(-7\right)^{0}$$

Calculate -\frac{1}{3} to the power of -3 and get -27.

$$-\frac{74}{25}-27+\left(-7\right)^{0}$$

Subtract 27 from -\frac{74}{25} to get -\frac{749}{25}.

$$-\frac{749}{25}+\left(-7\right)^{0}$$

Calculate -7 to the power of 0 and get 1.

$$-\frac{749}{25}+1$$

Add -\frac{749}{25} and 1 to get -\frac{724}{25}.

$$-\frac{724}{25}$$

Factor

$$-\frac{724}{25} = -28\frac{24}{25} = -28.96$$