Solve 8/75div(-2/5)^2+(1-2/3)^3*(-3)^4-2^4*(-1/2)

$$\frac { 8 } { 75 } \div ( - \frac { 2 } { 5 } ) ^ { 2 } + ( 1 - \frac { 2 } { 3 } ) ^ { 3 } \times ( - 3 ) ^ { 4 } - 2 ^ { 4 } \times ( - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{35}{3}\approx 11.666666667$$

Solution Steps

Calculate -\frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{\frac{8}{75}}{\frac{4}{25}}+\left(1-\frac{2}{3}\right)^{3}\left(-3\right)^{4}-2^{4}\left(-\frac{1}{2}\right)$$

Divide \frac{8}{75} by \frac{4}{25} by multiplying \frac{8}{75} by the reciprocal of \frac{4}{25}.

$$\frac{8}{75}\times \frac{25}{4}+\left(1-\frac{2}{3}\right)^{3}\left(-3\right)^{4}-2^{4}\left(-\frac{1}{2}\right)$$

Multiply \frac{8}{75} and \frac{25}{4} to get \frac{2}{3}.

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

Subtract \frac{2}{3} from 1 to get \frac{1}{3}.

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

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{2}{3}+\frac{1}{27}\left(-3\right)^{4}-2^{4}\left(-\frac{1}{2}\right)$$

Calculate -3 to the power of 4 and get 81.

$$\frac{2}{3}+\frac{1}{27}\times 81-2^{4}\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{27} and 81 to get 3.

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

Add \frac{2}{3} and 3 to get \frac{11}{3}.

$$\frac{11}{3}-2^{4}\left(-\frac{1}{2}\right)$$

Calculate 2 to the power of 4 and get 16.

$$\frac{11}{3}-16\left(-\frac{1}{2}\right)$$

Multiply 16 and -\frac{1}{2} to get -8.

$$\frac{11}{3}-\left(-8\right)$$

The opposite of -8 is 8.

$$\frac{11}{3}+8$$

Add \frac{11}{3} and 8 to get \frac{35}{3}.

$$\frac{35}{3}$$

Factor

$$\frac{5 \cdot 7}{3} = 11\frac{2}{3} = 11.666666666666666$$