Solve (3/4)^6*(16/3)^6:(16/9)^6:(2/3)^6

$$( \frac { 3 } { 4 } ) ^ { 6 } \cdot ( \frac { 16 } { 3 } ) ^ { 6 } : ( \frac { 16 } { 9 } ) ^ { 6 } : ( \frac { 2 } { 3 } ) ^ { 6 }$$

Evaluate

$$\frac{387420489}{262144}\approx 1477.891880035$$

Solution Steps

Calculate \frac{3}{4} to the power of 6 and get \frac{729}{4096}.

$$\frac{\frac{\frac{729}{4096}\times \left(\frac{16}{3}\right)^{6}}{\left(\frac{16}{9}\right)^{6}}}{\left(\frac{2}{3}\right)^{6}}$$

Calculate \frac{16}{3} to the power of 6 and get \frac{16777216}{729}.

$$\frac{\frac{\frac{729}{4096}\times \frac{16777216}{729}}{\left(\frac{16}{9}\right)^{6}}}{\left(\frac{2}{3}\right)^{6}}$$

Multiply \frac{729}{4096} times \frac{16777216}{729} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{729\times 16777216}{4096\times 729}}{\left(\frac{16}{9}\right)^{6}}}{\left(\frac{2}{3}\right)^{6}}$$

Cancel out 729 in both numerator and denominator.

$$\frac{\frac{\frac{16777216}{4096}}{\left(\frac{16}{9}\right)^{6}}}{\left(\frac{2}{3}\right)^{6}}$$

Divide 16777216 by 4096 to get 4096.

$$\frac{\frac{4096}{\left(\frac{16}{9}\right)^{6}}}{\left(\frac{2}{3}\right)^{6}}$$

Calculate \frac{16}{9} to the power of 6 and get \frac{16777216}{531441}.

$$\frac{\frac{4096}{\frac{16777216}{531441}}}{\left(\frac{2}{3}\right)^{6}}$$

Divide 4096 by \frac{16777216}{531441} by multiplying 4096 by the reciprocal of \frac{16777216}{531441}.

$$\frac{4096\times \frac{531441}{16777216}}{\left(\frac{2}{3}\right)^{6}}$$

Express 4096\times \frac{531441}{16777216} as a single fraction.

$$\frac{\frac{4096\times 531441}{16777216}}{\left(\frac{2}{3}\right)^{6}}$$

Multiply 4096 and 531441 to get 2176782336.

$$\frac{\frac{2176782336}{16777216}}{\left(\frac{2}{3}\right)^{6}}$$

Reduce the fraction \frac{2176782336}{16777216} to lowest terms by extracting and canceling out 4096.

$$\frac{\frac{531441}{4096}}{\left(\frac{2}{3}\right)^{6}}$$

Calculate \frac{2}{3} to the power of 6 and get \frac{64}{729}.

$$\frac{\frac{531441}{4096}}{\frac{64}{729}}$$

Divide \frac{531441}{4096} by \frac{64}{729} by multiplying \frac{531441}{4096} by the reciprocal of \frac{64}{729}.

$$\frac{531441}{4096}\times \frac{729}{64}$$

Multiply \frac{531441}{4096} times \frac{729}{64} by multiplying numerator times numerator and denominator times denominator.

$$\frac{531441\times 729}{4096\times 64}$$

Do the multiplications in the fraction \frac{531441\times 729}{4096\times 64}.

$$\frac{387420489}{262144}$$

Factor

$$\frac{3 ^ {18}}{2 ^ {18}} = 1477\frac{233801}{262144} = 1477.8918800354004$$