Solve ((-2)^{-3}+16^{-1}):6^{-2}+2^{3}*-1^-8-2^-2/2^3-2^4

$$( ( - 2 ) ^ { - 3 } + 16 ^ { - 1 } ) : 6 ^ { - 2 } + 2 ^ { 3 } \cdot \frac { - 1 ^ { - 8 } - 2 ^ { - 2 } } { 2 ^ { 3 } - 2 ^ { 4 } }$$

Evaluate

$$-1$$

Solution Steps

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

$$\frac{-\frac{1}{8}+16^{-1}}{6^{-2}}+2^{3}\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

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

$$\frac{-\frac{1}{8}+\frac{1}{16}}{6^{-2}}+2^{3}\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

Add -\frac{1}{8} and \frac{1}{16} to get -\frac{1}{16}.

$$\frac{-\frac{1}{16}}{6^{-2}}+2^{3}\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{-\frac{1}{16}}{\frac{1}{36}}+2^{3}\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

Divide -\frac{1}{16} by \frac{1}{36} by multiplying -\frac{1}{16} by the reciprocal of \frac{1}{36}.

$$-\frac{1}{16}\times 36+2^{3}\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

Multiply -\frac{1}{16} and 36 to get -\frac{9}{4}.

$$-\frac{9}{4}+2^{3}\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{9}{4}+8\times \frac{-1^{-8}-2^{-2}}{2^{3}-2^{4}}$$

Calculate 1 to the power of -8 and get 1.

$$-\frac{9}{4}+8\times \frac{-1-2^{-2}}{2^{3}-2^{4}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$-\frac{9}{4}+8\times \frac{-1-\frac{1}{4}}{2^{3}-2^{4}}$$

Subtract \frac{1}{4} from -1 to get -\frac{5}{4}.

$$-\frac{9}{4}+8\times \frac{-\frac{5}{4}}{2^{3}-2^{4}}$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{9}{4}+8\times \frac{-\frac{5}{4}}{8-2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$-\frac{9}{4}+8\times \frac{-\frac{5}{4}}{8-16}$$

Subtract 16 from 8 to get -8.

$$-\frac{9}{4}+8\times \frac{-\frac{5}{4}}{-8}$$

Express \frac{-\frac{5}{4}}{-8} as a single fraction.

$$-\frac{9}{4}+8\times \frac{-5}{4\left(-8\right)}$$

Multiply 4 and -8 to get -32.

$$-\frac{9}{4}+8\times \frac{-5}{-32}$$

Fraction \frac{-5}{-32} can be simplified to \frac{5}{32} by removing the negative sign from both the numerator and the denominator.

$$-\frac{9}{4}+8\times \frac{5}{32}$$

Multiply 8 and \frac{5}{32} to get \frac{5}{4}.

$$-\frac{9}{4}+\frac{5}{4}$$

Add -\frac{9}{4} and \frac{5}{4} to get -1.

$$-1$$

Factor

$$-1$$