Solve {left(15/2right)}^3*{left(2/5right)}^2

$${ \left( \frac{ 15 }{ 2 } \right) }^{ 3 } \times { \left( \frac{ 2 }{ 5 } \right) }^{ 2 }$$

Evaluate

$$\frac{135}{2}=67.5$$

Solution Steps

Calculate \frac{15}{2} to the power of 3 and get \frac{3375}{8}.

$$\frac{3375}{8}\times \left(\frac{2}{5}\right)^{2}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{3375}{8}\times \frac{4}{25}$$

Multiply \frac{3375}{8} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3375\times 4}{8\times 25}$$

Do the multiplications in the fraction \frac{3375\times 4}{8\times 25}.

$$\frac{13500}{200}$$

Reduce the fraction \frac{13500}{200} to lowest terms by extracting and canceling out 100.

$$\frac{135}{2}$$

Factor

$$\frac{3 ^ {3} \cdot 5}{2} = 67\frac{1}{2} = 67.5$$