Solve (1/2^-3-1/2^-1)^-3

$$( \frac { 1 } { 2 ^ { - 3 } } - \frac { 1 } { 2 ^ { - 1 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{216}\approx 0.00462963$$

Solution Steps

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

$$\left(\frac{1}{\frac{1}{8}}-\frac{1}{2^{-1}}\right)^{-3}$$

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

$$\left(1\times 8-\frac{1}{2^{-1}}\right)^{-3}$$

Multiply 1 and 8 to get 8.

$$\left(8-\frac{1}{2^{-1}}\right)^{-3}$$

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

$$\left(8-\frac{1}{\frac{1}{2}}\right)^{-3}$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$\left(8-1\times 2\right)^{-3}$$

Multiply 1 and 2 to get 2.

$$\left(8-2\right)^{-3}$$

Subtract 2 from 8 to get 6.

$$6^{-3}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{1}{216}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3 ^ {3}} = 0.004629629629629629$$