Solve -4/6*{left(8/6right)}^8{left(-3/2right)}^2{left(75/100right)}^3

$$- \frac{ 4 }{ 6 } \times { \left( \frac{ 8 }{ 6 } \right) }^{ 8 } { \left(- \frac{ 3 }{ 2 } \right) }^{ 2 } { \left( \frac{ 75 }{ 100 } \right) }^{ 3 }$$

Evaluate

$$-\frac{512}{81}\approx -6.320987654$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}\times \left(\frac{8}{6}\right)^{8}\left(-\frac{3}{2}\right)^{2}\times \left(\frac{75}{100}\right)^{3}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}\times \left(\frac{4}{3}\right)^{8}\left(-\frac{3}{2}\right)^{2}\times \left(\frac{75}{100}\right)^{3}$$

Calculate \frac{4}{3} to the power of 8 and get \frac{65536}{6561}.

$$-\frac{2}{3}\times \frac{65536}{6561}\left(-\frac{3}{2}\right)^{2}\times \left(\frac{75}{100}\right)^{3}$$

Multiply -\frac{2}{3} and \frac{65536}{6561} to get -\frac{131072}{19683}.

$$-\frac{131072}{19683}\left(-\frac{3}{2}\right)^{2}\times \left(\frac{75}{100}\right)^{3}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$-\frac{131072}{19683}\times \frac{9}{4}\times \left(\frac{75}{100}\right)^{3}$$

Multiply -\frac{131072}{19683} and \frac{9}{4} to get -\frac{32768}{2187}.

$$-\frac{32768}{2187}\times \left(\frac{75}{100}\right)^{3}$$

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{32768}{2187}\times \left(\frac{3}{4}\right)^{3}$$

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$-\frac{32768}{2187}\times \frac{27}{64}$$

Multiply -\frac{32768}{2187} and \frac{27}{64} to get -\frac{512}{81}.

$$-\frac{512}{81}$$

Factor

$$-\frac{512}{81} = -6\frac{26}{81} = -6.320987654320987$$