Solve (4/3)^4div(2/9)^2

$$( \frac { 4 } { 3 } ) ^ { 4 } \div ( \frac { 2 } { 9 } ) ^ { 2 }$$

Evaluate

$$64$$

Solution Steps

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

$$\frac{\frac{256}{81}}{\left(\frac{2}{9}\right)^{2}}$$

Calculate \frac{2}{9} to the power of 2 and get \frac{4}{81}.

$$\frac{\frac{256}{81}}{\frac{4}{81}}$$

Divide \frac{256}{81} by \frac{4}{81} by multiplying \frac{256}{81} by the reciprocal of \frac{4}{81}.

$$\frac{256}{81}\times \frac{81}{4}$$

Multiply \frac{256}{81} times \frac{81}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{256\times 81}{81\times 4}$$

Cancel out 81 in both numerator and denominator.

$$\frac{256}{4}$$

Divide 256 by 4 to get 64.

$$64$$

Factor

$$2^{6}$$