Solve (81/16)^-3/4*[(25/9)^-3/2+(5/2)^-3]

$$( \frac { 81 } { 16 } ) ^ { - 3 / 4 } \times [ ( \frac { 25 } { 9 } ) ^ { - 3 / 2 } + ( \frac { 5 } { 2 } ) ^ { - 3 } ]$$

Evaluate

$$\frac{56}{675}\approx 0.082962963$$

Solution Steps

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

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

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

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

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

$$\frac{8}{27}\left(\frac{27}{125}+\frac{8}{125}\right)$$

Add \frac{27}{125} and \frac{8}{125} to get \frac{7}{25}.

$$\frac{8}{27}\times \frac{7}{25}$$

Multiply \frac{8}{27} and \frac{7}{25} to get \frac{56}{675}.

$$\frac{56}{675}$$

Factor

$$\frac{2 ^ {3} \cdot 7}{3 ^ {3} \cdot 5 ^ {2}} = 0.08296296296296296$$