Solve (81)^frac{3{4}}quadtext{(ii)}(1/32)^-frac{4{5}}quadtext{(iii)}(125)^-frac{1{3}}

$$( 81 ) ^ { \frac { 3 } { 4 } } \quad \text { (ii) } ( \frac { 1 } { 32 } ) ^ { - \frac { 4 } { 5 } } \quad \text { (iii) } ( 125 ) ^ { - \frac { 1 } { 3 } }$$

Evaluate

$$\frac{432}{5}i=86.4i$$

Solution Steps

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

$$27ii\times \left(\frac{1}{32}\right)^{-\frac{4}{5}}iii\times 125^{-\frac{1}{3}}$$

Multiply 27i and i to get -27.

$$-27\times \left(\frac{1}{32}\right)^{-\frac{4}{5}}iii\times 125^{-\frac{1}{3}}$$

Calculate \frac{1}{32} to the power of -\frac{4}{5} and get 16.

$$-27\times \left(16i\right)ii\times 125^{-\frac{1}{3}}$$

Multiply -27 and 16i to get -432i.

$$-432iii\times 125^{-\frac{1}{3}}$$

Multiply -432i and i to get 432.

$$432i\times 125^{-\frac{1}{3}}$$

Calculate 125 to the power of -\frac{1}{3} and get \frac{1}{5}.

$$432i\times \frac{1}{5}$$

Multiply 432i and \frac{1}{5} to get \frac{432}{5}i.

$$\frac{432}{5}i$$

Real Part

$$0$$

Solution Steps

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

$$Re(27ii\times \left(\frac{1}{32}\right)^{-\frac{4}{5}}iii\times 125^{-\frac{1}{3}})$$

Multiply 27i and i to get -27.

$$Re(-27\times \left(\frac{1}{32}\right)^{-\frac{4}{5}}iii\times 125^{-\frac{1}{3}})$$

Calculate \frac{1}{32} to the power of -\frac{4}{5} and get 16.

$$Re(-27\times \left(16i\right)ii\times 125^{-\frac{1}{3}})$$

Multiply -27 and 16i to get -432i.

$$Re(-432iii\times 125^{-\frac{1}{3}})$$

Multiply -432i and i to get 432.

$$Re(432i\times 125^{-\frac{1}{3}})$$

Calculate 125 to the power of -\frac{1}{3} and get \frac{1}{5}.

$$Re(432i\times \frac{1}{5})$$

Multiply 432i and \frac{1}{5} to get \frac{432}{5}i.

$$Re(\frac{432}{5}i)$$

The real part of \frac{432}{5}i is 0.

$$0$$