Solve (8^{-1})^{-1}(text{ii})(2^-1*3^-1)^2*(-3/8)^-1

$$( 8 ^ { - 1 } ) ^ { - 1 } ( \text { ii } ) ( 2 ^ { - 1 } \times 3 ^ { - 1 } ) ^ { 2 } \times ( - \frac { 3 } { 8 } ) ^ { - 1 }$$

Evaluate

$$\frac{16}{27}\approx 0.592592593$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and -1 to get 1.

$$8^{1}ii\times \left(2^{-1}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1}$$

Calculate 8 to the power of 1 and get 8.

$$8ii\times \left(2^{-1}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1}$$

Multiply 8i and i to get -8.

$$-8\times \left(2^{-1}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$-8\times \left(\frac{1}{2}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$-8\times \left(\frac{1}{2}\times \frac{1}{3}\right)^{2}\left(-\frac{3}{8}\right)^{-1}$$

Multiply \frac{1}{2} and \frac{1}{3} to get \frac{1}{6}.

$$-8\times \left(\frac{1}{6}\right)^{2}\left(-\frac{3}{8}\right)^{-1}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$-8\times \frac{1}{36}\left(-\frac{3}{8}\right)^{-1}$$

Multiply -8 and \frac{1}{36} to get -\frac{2}{9}.

$$-\frac{2}{9}\left(-\frac{3}{8}\right)^{-1}$$

Calculate -\frac{3}{8} to the power of -1 and get -\frac{8}{3}.

$$-\frac{2}{9}\left(-\frac{8}{3}\right)$$

Multiply -\frac{2}{9} and -\frac{8}{3} to get \frac{16}{27}.

$$\frac{16}{27}$$

Real Part

$$\frac{16}{27} = 0.5925925925925926$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and -1 to get 1.

$$Re(8^{1}ii\times \left(2^{-1}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1})$$

Calculate 8 to the power of 1 and get 8.

$$Re(8ii\times \left(2^{-1}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1})$$

Multiply 8i and i to get -8.

$$Re(-8\times \left(2^{-1}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1})$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$Re(-8\times \left(\frac{1}{2}\times 3^{-1}\right)^{2}\left(-\frac{3}{8}\right)^{-1})$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$Re(-8\times \left(\frac{1}{2}\times \frac{1}{3}\right)^{2}\left(-\frac{3}{8}\right)^{-1})$$

Multiply \frac{1}{2} and \frac{1}{3} to get \frac{1}{6}.

$$Re(-8\times \left(\frac{1}{6}\right)^{2}\left(-\frac{3}{8}\right)^{-1})$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$Re(-8\times \frac{1}{36}\left(-\frac{3}{8}\right)^{-1})$$

Multiply -8 and \frac{1}{36} to get -\frac{2}{9}.

$$Re(-\frac{2}{9}\left(-\frac{3}{8}\right)^{-1})$$

Calculate -\frac{3}{8} to the power of -1 and get -\frac{8}{3}.

$$Re(-\frac{2}{9}\left(-\frac{8}{3}\right))$$

Multiply -\frac{2}{9} and -\frac{8}{3} to get \frac{16}{27}.

$$Re(\frac{16}{27})$$

The real part of \frac{16}{27} is \frac{16}{27}.

$$\frac{16}{27}$$