Solve 125/128*{left(2/3^right)}^6*-{left(5/3^right)}^-3

$$\frac{ 125 }{ 128 } \times { \left( \frac{ 2 }{ { 3 }^{ } } \right) }^{ 6 } \times - { \left( \frac{ 5 }{ { 3 }^{ } } \right) }^{ -3 }$$

Evaluate

$$-\frac{1}{54}\approx -0.018518519$$

Solution Steps

Calculate 3 to the power of 1 and get 3.

$$\frac{125}{128}\times \left(\frac{2}{3}\right)^{6}\left(-\left(\frac{5}{3^{1}}\right)^{-3}\right)$$

Calculate \frac{2}{3} to the power of 6 and get \frac{64}{729}.

$$\frac{125}{128}\times \frac{64}{729}\left(-\left(\frac{5}{3^{1}}\right)^{-3}\right)$$

Multiply \frac{125}{128} and \frac{64}{729} to get \frac{125}{1458}.

$$\frac{125}{1458}\left(-\left(\frac{5}{3^{1}}\right)^{-3}\right)$$

Calculate 3 to the power of 1 and get 3.

$$\frac{125}{1458}\left(-\left(\frac{5}{3}\right)^{-3}\right)$$

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

$$\frac{125}{1458}\left(-\frac{27}{125}\right)$$

Multiply \frac{125}{1458} and -\frac{27}{125} to get -\frac{1}{54}.

$$-\frac{1}{54}$$

Factor

$$-\frac{1}{54} = -0.018518518518518517$$