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

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

Evaluate

$$-8$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

Calculate -2 to the power of -3 and get -\frac{1}{8}.

$$-\frac{1}{8}-\left(-\frac{1}{3}\right)^{-2}+2^{-3}+\left(-\frac{5}{7}\right)^{0}$$

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

$$-\frac{1}{8}-9+2^{-3}+\left(-\frac{5}{7}\right)^{0}$$

Subtract 9 from -\frac{1}{8} to get -\frac{73}{8}.

$$-\frac{73}{8}+2^{-3}+\left(-\frac{5}{7}\right)^{0}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$-\frac{73}{8}+\frac{1}{8}+\left(-\frac{5}{7}\right)^{0}$$

Add -\frac{73}{8} and \frac{1}{8} to get -9.

$$-9+\left(-\frac{5}{7}\right)^{0}$$

Calculate -\frac{5}{7} to the power of 0 and get 1.

$$-9+1$$

Add -9 and 1 to get -8.

$$-8$$

Factor

$$-8$$