Solve (21/4)^-frac{3{2}}*(33/8)^-frac{1{3}}

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

Evaluate

$$\frac{16}{81}\approx 0.197530864$$

Solution Steps

Multiply 2 and 4 to get 8.

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

Add 8 and 1 to get 9.

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

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

$$\frac{8}{27}\times \left(\frac{3\times 8+3}{8}\right)^{-\frac{1}{3}}$$

Multiply 3 and 8 to get 24.

$$\frac{8}{27}\times \left(\frac{24+3}{8}\right)^{-\frac{1}{3}}$$

Add 24 and 3 to get 27.

$$\frac{8}{27}\times \left(\frac{27}{8}\right)^{-\frac{1}{3}}$$

Calculate \frac{27}{8} to the power of -\frac{1}{3} and get \frac{2}{3}.

$$\frac{8}{27}\times \frac{2}{3}$$

Multiply \frac{8}{27} and \frac{2}{3} to get \frac{16}{81}.

$$\frac{16}{81}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {4}} = 0.19753086419753085$$