Solve 2(text{ii})(81)^3/4-(1/32)^-2/5+(8)^1/3(1/2)^-1

$$2 ( \text { ii } ) ( 81 ) ^ { 3 / 4 } - ( \frac { 1 } { 32 } ) ^ { - 2 / 5 } + ( 8 ) ^ { 1 / 3 } ( \frac { 1 } { 2 } ) ^ { - 1 }$$

Evaluate

$$-54$$

Solution Steps

Multiply 2i and i to get -2.

$$-2\times 81^{\frac{3}{4}}-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1}$$

Calculate 81 to the power of \frac{3}{4} and get 27.

$$-2\times 27-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1}$$

Multiply -2 and 27 to get -54.

$$-54-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1}$$

Calculate \frac{1}{32} to the power of -\frac{2}{5} and get 4.

$$-54-4+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1}$$

Subtract 4 from -54 to get -58.

$$-58+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1}$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$-58+2\times \left(\frac{1}{2}\right)^{-1}$$

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

$$-58+2\times 2$$

Multiply 2 and 2 to get 4.

$$-58+4$$

Add -58 and 4 to get -54.

$$-54$$

Real Part

$$-54$$

Solution Steps

Multiply 2i and i to get -2.

$$Re(-2\times 81^{\frac{3}{4}}-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1})$$

Calculate 81 to the power of \frac{3}{4} and get 27.

$$Re(-2\times 27-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1})$$

Multiply -2 and 27 to get -54.

$$Re(-54-\left(\frac{1}{32}\right)^{-\frac{2}{5}}+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1})$$

Calculate \frac{1}{32} to the power of -\frac{2}{5} and get 4.

$$Re(-54-4+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1})$$

Subtract 4 from -54 to get -58.

$$Re(-58+8^{\frac{1}{3}}\times \left(\frac{1}{2}\right)^{-1})$$

Calculate 8 to the power of \frac{1}{3} and get 2.

$$Re(-58+2\times \left(\frac{1}{2}\right)^{-1})$$

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

$$Re(-58+2\times 2)$$

Multiply 2 and 2 to get 4.

$$Re(-58+4)$$

Add -58 and 4 to get -54.

$$Re(-54)$$

The real part of -54 is -54.

$$-54$$