Solve (2/5)^4div(3/2)^4

$$( \frac { 2 } { 5 } ) ^ { 4 } \div ( \frac { 3 } { 2 } ) ^ { 4 }$$

Evaluate

$$\frac{256}{50625}\approx 0.00505679$$

Solution Steps

Calculate \frac{2}{5} to the power of 4 and get \frac{16}{625}.

$$\frac{\frac{16}{625}}{\left(\frac{3}{2}\right)^{4}}$$

Calculate \frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$\frac{\frac{16}{625}}{\frac{81}{16}}$$

Divide \frac{16}{625} by \frac{81}{16} by multiplying \frac{16}{625} by the reciprocal of \frac{81}{16}.

$$\frac{16}{625}\times \frac{16}{81}$$

Multiply \frac{16}{625} times \frac{16}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 16}{625\times 81}$$

Do the multiplications in the fraction \frac{16\times 16}{625\times 81}.

$$\frac{256}{50625}$$

Factor

$$\frac{2 ^ {8}}{3 ^ {4} \cdot 5 ^ {4}} = 0.00505679012345679$$