Solve frac{2^{-1}+2^{-2}+36^-frac{1{2}}}{81^frac{3{4}}+16^-frac{1{4}}-1^-100}

$$\frac { 2 ^ { - 1 } + 2 ^ { - 2 } + 36 ^ { - \frac { 1 } { 2 } } } { 81 ^ { \frac { 3 } { 4 } } + 16 ^ { - \frac { 1 } { 4 } } - 1 ^ { - 100 } }$$

Evaluate

$$\frac{11}{318}\approx 0.034591195$$

Solution Steps

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

$$\frac{\frac{1}{2}+2^{-2}+36^{-\frac{1}{2}}}{81^{\frac{3}{4}}+16^{-\frac{1}{4}}-1^{-100}}$$

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

$$\frac{\frac{1}{2}+\frac{1}{4}+36^{-\frac{1}{2}}}{81^{\frac{3}{4}}+16^{-\frac{1}{4}}-1^{-100}}$$

Add \frac{1}{2} and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\frac{3}{4}+36^{-\frac{1}{2}}}{81^{\frac{3}{4}}+16^{-\frac{1}{4}}-1^{-100}}$$

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

$$\frac{\frac{3}{4}+\frac{1}{6}}{81^{\frac{3}{4}}+16^{-\frac{1}{4}}-1^{-100}}$$

Add \frac{3}{4} and \frac{1}{6} to get \frac{11}{12}.

$$\frac{\frac{11}{12}}{81^{\frac{3}{4}}+16^{-\frac{1}{4}}-1^{-100}}$$

Calculate 81 to the power of \frac{3}{4} and get 27.

$$\frac{\frac{11}{12}}{27+16^{-\frac{1}{4}}-1^{-100}}$$

Calculate 16 to the power of -\frac{1}{4} and get \frac{1}{2}.

$$\frac{\frac{11}{12}}{27+\frac{1}{2}-1^{-100}}$$

Add 27 and \frac{1}{2} to get \frac{55}{2}.

$$\frac{\frac{11}{12}}{\frac{55}{2}-1^{-100}}$$

Calculate 1 to the power of -100 and get 1.

$$\frac{\frac{11}{12}}{\frac{55}{2}-1}$$

Subtract 1 from \frac{55}{2} to get \frac{53}{2}.

$$\frac{\frac{11}{12}}{\frac{53}{2}}$$

Divide \frac{11}{12} by \frac{53}{2} by multiplying \frac{11}{12} by the reciprocal of \frac{53}{2}.

$$\frac{11}{12}\times \frac{2}{53}$$

Multiply \frac{11}{12} and \frac{2}{53} to get \frac{11}{318}.

$$\frac{11}{318}$$

Factor

$$\frac{11}{2 \cdot 3 \cdot 53} = 0.03459119496855346$$