Solve {left(4/5right)}^3*{left(3/2right)}^3*{left(5/3right)}^3

$${ \left( \frac{ 4 }{ 5 } \right) }^{ 3 } \times { \left( \frac{ 3 }{ 2 } \right) }^{ 3 } \times { \left( \frac{ 5 }{ 3 } \right) }^{ 3 }$$

Evaluate

$$8$$

Solution Steps

Calculate \frac{4}{5} to the power of 3 and get \frac{64}{125}.

$$\frac{64}{125}\times \left(\frac{3}{2}\right)^{3}\times \left(\frac{5}{3}\right)^{3}$$

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

$$\frac{64}{125}\times \frac{27}{8}\times \left(\frac{5}{3}\right)^{3}$$

Multiply \frac{64}{125} times \frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 27}{125\times 8}\times \left(\frac{5}{3}\right)^{3}$$

Do the multiplications in the fraction \frac{64\times 27}{125\times 8}.

$$\frac{1728}{1000}\times \left(\frac{5}{3}\right)^{3}$$

Reduce the fraction \frac{1728}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{216}{125}\times \left(\frac{5}{3}\right)^{3}$$

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

$$\frac{216}{125}\times \frac{125}{27}$$

Multiply \frac{216}{125} times \frac{125}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{216\times 125}{125\times 27}$$

Cancel out 125 in both numerator and denominator.

$$\frac{216}{27}$$

Divide 216 by 27 to get 8.

$$8$$

Factor

$$2^{3}$$