Solve (2-1/3)^0-(1/8)^-frac{1{3}}+(4/9)^-frac{3{2}}

$$( 2 - \frac { 1 } { 3 } ) ^ { 0 } - ( \frac { 1 } { 8 } ) ^ { - \frac { 1 } { 3 } } + ( \frac { 4 } { 9 } ) ^ { - \frac { 3 } { 2 } }$$

Evaluate

$$\frac{19}{8}=2.375$$

Solution Steps

Subtract \frac{1}{3} from 2 to get \frac{5}{3}.

$$\left(\frac{5}{3}\right)^{0}-\left(\frac{1}{8}\right)^{-\frac{1}{3}}+\left(\frac{4}{9}\right)^{-\frac{3}{2}}$$

Calculate \frac{5}{3} to the power of 0 and get 1.

$$1-\left(\frac{1}{8}\right)^{-\frac{1}{3}}+\left(\frac{4}{9}\right)^{-\frac{3}{2}}$$

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

$$1-2+\left(\frac{4}{9}\right)^{-\frac{3}{2}}$$

Subtract 2 from 1 to get -1.

$$-1+\left(\frac{4}{9}\right)^{-\frac{3}{2}}$$

Calculate \frac{4}{9} to the power of -\frac{3}{2} and get \frac{27}{8}.

$$-1+\frac{27}{8}$$

Add -1 and \frac{27}{8} to get \frac{19}{8}.

$$\frac{19}{8}$$

Factor

$$\frac{19}{2 ^ {3}} = 2\frac{3}{8} = 2.375$$