Solve [(-2)^-1*5]^-3/5^-5=

$$\frac { [ ( - 2 ) ^ { - 1 } \cdot 5 ] ^ { - 3 } } { 5 ^ { - 5 } } =$$

Evaluate

$$-200$$

Solution Steps

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

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

Multiply -\frac{1}{2} and 5 to get -\frac{5}{2}.

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

Calculate -\frac{5}{2} to the power of -3 and get -\frac{8}{125}.

$$\frac{-\frac{8}{125}}{5^{-5}}$$

Calculate 5 to the power of -5 and get \frac{1}{3125}.

$$\frac{-\frac{8}{125}}{\frac{1}{3125}}$$

Divide -\frac{8}{125} by \frac{1}{3125} by multiplying -\frac{8}{125} by the reciprocal of \frac{1}{3125}.

$$-\frac{8}{125}\times 3125$$

Multiply -\frac{8}{125} and 3125 to get -200.

$$-200$$

Factor

$$-200$$