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

$$( \frac { 1 } { 3 } ) ^ { - 3 } \times ( - 2 ) ^ { 3 } \times ( \frac { - 1 } { 3 } ) ^ { - 2 } \times ( \frac { 2 } { 3 } ) ^ { - 3 }$$

Evaluate

$$-6561$$

Solution Steps

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

$$27\left(-2\right)^{3}\times \left(\frac{-1}{3}\right)^{-2}\times \left(\frac{2}{3}\right)^{-3}$$

Calculate -2 to the power of 3 and get -8.

$$27\left(-8\right)\times \left(\frac{-1}{3}\right)^{-2}\times \left(\frac{2}{3}\right)^{-3}$$

Multiply 27 and -8 to get -216.

$$-216\times \left(\frac{-1}{3}\right)^{-2}\times \left(\frac{2}{3}\right)^{-3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$-216\left(-\frac{1}{3}\right)^{-2}\times \left(\frac{2}{3}\right)^{-3}$$

Calculate -\frac{1}{3} to the power of -2 and get 9.

$$-216\times 9\times \left(\frac{2}{3}\right)^{-3}$$

Multiply -216 and 9 to get -1944.

$$-1944\times \left(\frac{2}{3}\right)^{-3}$$

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

$$-1944\times \frac{27}{8}$$

Multiply -1944 and \frac{27}{8} to get -6561.

$$-6561$$

Factor

$$-6561$$