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

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

Evaluate

$$214$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

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

$$\frac{4}{\frac{1}{36}}+\frac{1}{256^{\frac{-3}{4}}}+\frac{2}{243^{\frac{-1}{5}}}$$

Divide 4 by \frac{1}{36} by multiplying 4 by the reciprocal of \frac{1}{36}.

$$4\times 36+\frac{1}{256^{\frac{-3}{4}}}+\frac{2}{243^{\frac{-1}{5}}}$$

Multiply 4 and 36 to get 144.

$$144+\frac{1}{256^{\frac{-3}{4}}}+\frac{2}{243^{\frac{-1}{5}}}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$144+\frac{1}{256^{-\frac{3}{4}}}+\frac{2}{243^{\frac{-1}{5}}}$$

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

$$144+\frac{1}{\frac{1}{64}}+\frac{2}{243^{\frac{-1}{5}}}$$

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

$$144+1\times 64+\frac{2}{243^{\frac{-1}{5}}}$$

Multiply 1 and 64 to get 64.

$$144+64+\frac{2}{243^{\frac{-1}{5}}}$$

Add 144 and 64 to get 208.

$$208+\frac{2}{243^{\frac{-1}{5}}}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$208+\frac{2}{243^{-\frac{1}{5}}}$$

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

$$208+\frac{2}{\frac{1}{3}}$$

Divide 2 by \frac{1}{3} by multiplying 2 by the reciprocal of \frac{1}{3}.

$$208+2\times 3$$

Multiply 2 and 3 to get 6.

$$208+6$$

Add 208 and 6 to get 214.

$$214$$

Factor

$$2\times 107$$