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

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

Evaluate

$$\frac{400}{81}\approx 4.938271605$$

Solution Steps

Calculate \frac{3}{4} to the power of -4 and get \frac{256}{81}.

$$\frac{\frac{256}{81}}{\left(\frac{5}{4}\right)^{-2}}$$

Calculate \frac{5}{4} to the power of -2 and get \frac{16}{25}.

$$\frac{\frac{256}{81}}{\frac{16}{25}}$$

Divide \frac{256}{81} by \frac{16}{25} by multiplying \frac{256}{81} by the reciprocal of \frac{16}{25}.

$$\frac{256}{81}\times \frac{25}{16}$$

Multiply \frac{256}{81} and \frac{25}{16} to get \frac{400}{81}.

$$\frac{400}{81}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {2}}{3 ^ {4}} = 4\frac{76}{81} = 4.938271604938271$$