Solve (8^frac{2{3}})^frac{-1{2}}-(81^frac{-3{4}})^frac{2{3}}

$$( 8 ^ { \frac { 2 } { 3 } } ) ^ { \frac { - 1 } { 2 } } - ( 81 ^ { \frac { - 3 } { 4 } } ) ^ { \frac { 2 } { 3 } }$$

Evaluate

$$\frac{7}{18}\approx 0.388888889$$

Solution Steps

Calculate 8 to the power of \frac{2}{3} and get 4.

$$4^{\frac{-1}{2}}-\left(81^{\frac{-3}{4}}\right)^{\frac{2}{3}}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$4^{-\frac{1}{2}}-\left(81^{\frac{-3}{4}}\right)^{\frac{2}{3}}$$

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

$$\frac{1}{2}-\left(81^{\frac{-3}{4}}\right)^{\frac{2}{3}}$$

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

$$\frac{1}{2}-\left(81^{-\frac{3}{4}}\right)^{\frac{2}{3}}$$

Calculate 81 to the power of -\frac{3}{4} and get \frac{1}{27}.

$$\frac{1}{2}-\left(\frac{1}{27}\right)^{\frac{2}{3}}$$

Calculate \frac{1}{27} to the power of \frac{2}{3} and get \frac{1}{9}.

$$\frac{1}{2}-\frac{1}{9}$$

Subtract \frac{1}{9} from \frac{1}{2} to get \frac{7}{18}.

$$\frac{7}{18}$$

Factor

$$\frac{7}{2 \cdot 3 ^ {2}} = 0.3888888888888889$$