Solve 3^2*9^4/27^5*8i^6

$$\frac { 3 ^ { 2 } \cdot 9 ^ { 4 } } { 27 ^ { 5 } \cdot 8 i ^ { 6 } }$$

Evaluate

$$-\frac{1}{1944}\approx -0.000514403$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{9\times 9^{4}}{27^{5}\times 8i^{6}}$$

Calculate 9 to the power of 4 and get 6561.

$$\frac{9\times 6561}{27^{5}\times 8i^{6}}$$

Multiply 9 and 6561 to get 59049.

$$\frac{59049}{27^{5}\times 8i^{6}}$$

Calculate 27 to the power of 5 and get 14348907.

$$\frac{59049}{14348907\times 8i^{6}}$$

Multiply 14348907 and 8 to get 114791256.

$$\frac{59049}{114791256i^{6}}$$

Calculate i to the power of 6 and get -1.

$$\frac{59049}{114791256\left(-1\right)}$$

Multiply 114791256 and -1 to get -114791256.

$$\frac{59049}{-114791256}$$

Reduce the fraction \frac{59049}{-114791256} to lowest terms by extracting and canceling out 59049.

$$-\frac{1}{1944}$$

Real Part

$$-\frac{1}{1944} = -0.00051440329218107$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$Re(\frac{9\times 9^{4}}{27^{5}\times 8i^{6}})$$

Calculate 9 to the power of 4 and get 6561.

$$Re(\frac{9\times 6561}{27^{5}\times 8i^{6}})$$

Multiply 9 and 6561 to get 59049.

$$Re(\frac{59049}{27^{5}\times 8i^{6}})$$

Calculate 27 to the power of 5 and get 14348907.

$$Re(\frac{59049}{14348907\times 8i^{6}})$$

Multiply 14348907 and 8 to get 114791256.

$$Re(\frac{59049}{114791256i^{6}})$$

Calculate i to the power of 6 and get -1.

$$Re(\frac{59049}{114791256\left(-1\right)})$$

Multiply 114791256 and -1 to get -114791256.

$$Re(\frac{59049}{-114791256})$$

Reduce the fraction \frac{59049}{-114791256} to lowest terms by extracting and canceling out 59049.

$$Re(-\frac{1}{1944})$$

The real part of -\frac{1}{1944} is -\frac{1}{1944}.

$$-\frac{1}{1944}$$