Solve 1/(216)^-2/3+1/(256)^-3/4+1/(243)^-1/5

$$\frac { 1 } { ( 216 ) ^ { - 2 / 3 } } + \frac { 1 } { ( 256 ) ^ { - 3 / 4 } } + \frac { 1 } { ( 243 ) ^ { - 1 / 5 } }$$

Evaluate

$$103$$

Solution Steps

Calculate 216 to the power of -\frac{2}{3} and get \frac{1}{36}.

$$\frac{1}{\frac{1}{36}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{243^{-\frac{1}{5}}}$$

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

$$1\times 36+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{243^{-\frac{1}{5}}}$$

Multiply 1 and 36 to get 36.

$$36+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{243^{-\frac{1}{5}}}$$

Calculate 256 to the power of -\frac{3}{4} and get \frac{1}{64}.

$$36+\frac{1}{\frac{1}{64}}+\frac{1}{243^{-\frac{1}{5}}}$$

Divide 1 by \frac{1}{64} by multiplying 1 by the reciprocal of \frac{1}{64}.

$$36+1\times 64+\frac{1}{243^{-\frac{1}{5}}}$$

Multiply 1 and 64 to get 64.

$$36+64+\frac{1}{243^{-\frac{1}{5}}}$$

Add 36 and 64 to get 100.

$$100+\frac{1}{243^{-\frac{1}{5}}}$$

Calculate 243 to the power of -\frac{1}{5} and get \frac{1}{3}.

$$100+\frac{1}{\frac{1}{3}}$$

Divide 1 by \frac{1}{3} by multiplying 1 by the reciprocal of \frac{1}{3}.

$$100+1\times 3$$

Multiply 1 and 3 to get 3.

$$100+3$$

Add 100 and 3 to get 103.

$$103$$

Factor

$$103$$