Solve (2/3)^-4*(5/3)^-3*(1/4)^-3*(3/5)^-5

$$( \frac { 2 } { 3 } ) ^ { - 4 } \cdot ( \frac { 5 } { 3 } ) ^ { - 3 } \cdot ( \frac { 1 } { 4 } ) ^ { - 3 } \cdot ( \frac { 3 } { 5 } ) ^ { - 5 }$$

Evaluate

$$900$$

Solution Steps

Calculate \frac{2}{3} to the power of -4 and get \frac{81}{16}.

$$\frac{81}{16}\times \left(\frac{5}{3}\right)^{-3}\times \left(\frac{1}{4}\right)^{-3}\times \left(\frac{3}{5}\right)^{-5}$$

Calculate \frac{5}{3} to the power of -3 and get \frac{27}{125}.

$$\frac{81}{16}\times \frac{27}{125}\times \left(\frac{1}{4}\right)^{-3}\times \left(\frac{3}{5}\right)^{-5}$$

Multiply \frac{81}{16} and \frac{27}{125} to get \frac{2187}{2000}.

$$\frac{2187}{2000}\times \left(\frac{1}{4}\right)^{-3}\times \left(\frac{3}{5}\right)^{-5}$$

Calculate \frac{1}{4} to the power of -3 and get 64.

$$\frac{2187}{2000}\times 64\times \left(\frac{3}{5}\right)^{-5}$$

Multiply \frac{2187}{2000} and 64 to get \frac{8748}{125}.

$$\frac{8748}{125}\times \left(\frac{3}{5}\right)^{-5}$$

Calculate \frac{3}{5} to the power of -5 and get \frac{3125}{243}.

$$\frac{8748}{125}\times \frac{3125}{243}$$

Multiply \frac{8748}{125} and \frac{3125}{243} to get 900.

$$900$$

Factor

$$2^{2}\times 3^{2}\times 5^{2}$$