Solve [-2*(-3/2)^2+2^2]:(-2)^2

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

Evaluate

$$-\frac{1}{8}=-0.125$$

Solution Steps

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{-2\times \frac{9}{4}+2^{2}}{\left(-2\right)^{2}}$$

Express -2\times \frac{9}{4} as a single fraction.

$$\frac{\frac{-2\times 9}{4}+2^{2}}{\left(-2\right)^{2}}$$

Multiply -2 and 9 to get -18.

$$\frac{\frac{-18}{4}+2^{2}}{\left(-2\right)^{2}}$$

Reduce the fraction \frac{-18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{9}{2}+2^{2}}{\left(-2\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-\frac{9}{2}+4}{\left(-2\right)^{2}}$$

Convert 4 to fraction \frac{8}{2}.

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

Since -\frac{9}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

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

Add -9 and 8 to get -1.

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

Calculate -2 to the power of 2 and get 4.

$$\frac{-\frac{1}{2}}{4}$$

Express \frac{-\frac{1}{2}}{4} as a single fraction.

$$\frac{-1}{2\times 4}$$

Multiply 2 and 4 to get 8.

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

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

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

Factor

$$-\frac{1}{8} = -0.125$$