Solve -16^-2*(-10)^-3/128^-4*32^4

$$- \frac { 16 ^ { - 2 } \cdot ( - 10 ) ^ { - 3 } } { 128 ^ { - 4 } \cdot 32 ^ { 4 } }$$

Evaluate

$$\frac{1}{1000}=0.001$$

Solution Steps

Calculate 16 to the power of -2 and get \frac{1}{256}.

$$-\frac{\frac{1}{256}\left(-10\right)^{-3}}{128^{-4}\times 32^{4}}$$

Calculate -10 to the power of -3 and get -\frac{1}{1000}.

$$-\frac{\frac{1}{256}\left(-\frac{1}{1000}\right)}{128^{-4}\times 32^{4}}$$

Multiply \frac{1}{256} and -\frac{1}{1000} to get -\frac{1}{256000}.

$$-\frac{-\frac{1}{256000}}{128^{-4}\times 32^{4}}$$

Calculate 128 to the power of -4 and get \frac{1}{268435456}.

$$-\frac{-\frac{1}{256000}}{\frac{1}{268435456}\times 32^{4}}$$

Calculate 32 to the power of 4 and get 1048576.

$$-\frac{-\frac{1}{256000}}{\frac{1}{268435456}\times 1048576}$$

Multiply \frac{1}{268435456} and 1048576 to get \frac{1}{256}.

$$-\frac{-\frac{1}{256000}}{\frac{1}{256}}$$

Divide -\frac{1}{256000} by \frac{1}{256} by multiplying -\frac{1}{256000} by the reciprocal of \frac{1}{256}.

$$-\left(-\frac{1}{256000}\times 256\right)$$

Multiply -\frac{1}{256000} and 256 to get -\frac{1}{1000}.

$$-\left(-\frac{1}{1000}\right)$$

The opposite of -\frac{1}{1000} is \frac{1}{1000}.

$$\frac{1}{1000}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 5 ^ {3}} = 0.001$$