Solve [5/4-(-2+3/4)^2]:(5/4)^2-(-2)^3}:[43/5-(-frac{4}{5})^2*(2-frac{3}{4})]

$$[ \frac { 5 } { 4 } - ( - 2 + \frac { 3 } { 4 } ) ^ { 2 } ] : ( \frac { 5 } { 4 } ) ^ { 2 } - ( - 2 ) ^ { 3 } \} : [ \frac { 43 } { 5 } - ( - \frac { 4 } { 5 } ) ^ { 2 } \cdot ( 2 - \frac { 3 } { 4 } ) ]$$

Evaluate

$$\frac{39}{5}=7.8$$

Solution Steps

Add -2 and \frac{3}{4} to get -\frac{5}{4}.

$$\frac{\frac{5}{4}-\left(-\frac{5}{4}\right)^{2}}{\left(\frac{5}{4}\right)^{2}}-\left(-2\right)^{3}$$

Calculate -\frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{\frac{5}{4}-\frac{25}{16}}{\left(\frac{5}{4}\right)^{2}}-\left(-2\right)^{3}$$

Subtract \frac{25}{16} from \frac{5}{4} to get -\frac{5}{16}.

$$\frac{-\frac{5}{16}}{\left(\frac{5}{4}\right)^{2}}-\left(-2\right)^{3}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{-\frac{5}{16}}{\frac{25}{16}}-\left(-2\right)^{3}$$

Divide -\frac{5}{16} by \frac{25}{16} by multiplying -\frac{5}{16} by the reciprocal of \frac{25}{16}.

$$-\frac{5}{16}\times \frac{16}{25}-\left(-2\right)^{3}$$

Multiply -\frac{5}{16} and \frac{16}{25} to get -\frac{1}{5}.

$$-\frac{1}{5}-\left(-2\right)^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-\frac{1}{5}-\left(-8\right)$$

The opposite of -8 is 8.

$$-\frac{1}{5}+8$$

Add -\frac{1}{5} and 8 to get \frac{39}{5}.

$$\frac{39}{5}$$

Factor

$$\frac{3 \cdot 13}{5} = 7\frac{4}{5} = 7.8$$