Solve (81/16)^-frac{3{4}}*{(25/9)^-frac{3{2}}div(5/2)^-3}

$$( \frac { 81 } { 16 } ) ^ { - \frac { 3 } { 4 } } \times \{ ( \frac { 25 } { 9 } ) ^ { - \frac { 3 } { 2 } } \div ( \frac { 5 } { 2 } ) ^ { - 3 } \}$$

Evaluate

$$1$$

Solution Steps

Calculate \frac{81}{16} to the power of -\frac{3}{4} and get \frac{8}{27}.

$$\frac{8}{27}\times \frac{\left(\frac{25}{9}\right)^{-\frac{3}{2}}}{\left(\frac{5}{2}\right)^{-3}}$$

Calculate \frac{25}{9} to the power of -\frac{3}{2} and get \frac{27}{125}.

$$\frac{8}{27}\times \frac{\frac{27}{125}}{\left(\frac{5}{2}\right)^{-3}}$$

Calculate \frac{5}{2} to the power of -3 and get \frac{8}{125}.

$$\frac{8}{27}\times \frac{\frac{27}{125}}{\frac{8}{125}}$$

Divide \frac{27}{125} by \frac{8}{125} by multiplying \frac{27}{125} by the reciprocal of \frac{8}{125}.

$$\frac{8}{27}\times \frac{27}{125}\times \frac{125}{8}$$

Multiply \frac{27}{125} and \frac{125}{8} to get \frac{27}{8}.

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

Multiply \frac{8}{27} and \frac{27}{8} to get 1.

$$1$$

Factor

$$1$$