Solve frac{-2^{2}+(2/3)^2}{-2^4+(-3)^2+4^2}

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

Evaluate

$$-\frac{32}{81}\approx -0.395061728$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

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

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

$$\frac{-4+\frac{4}{9}}{-2^{4}+\left(-3\right)^{2}+4^{2}}$$

Convert -4 to fraction -\frac{36}{9}.

$$\frac{-\frac{36}{9}+\frac{4}{9}}{-2^{4}+\left(-3\right)^{2}+4^{2}}$$

Since -\frac{36}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-36+4}{9}}{-2^{4}+\left(-3\right)^{2}+4^{2}}$$

Add -36 and 4 to get -32.

$$\frac{-\frac{32}{9}}{-2^{4}+\left(-3\right)^{2}+4^{2}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{-\frac{32}{9}}{-16+\left(-3\right)^{2}+4^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{-\frac{32}{9}}{-16+9+4^{2}}$$

Add -16 and 9 to get -7.

$$\frac{-\frac{32}{9}}{-7+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{-\frac{32}{9}}{-7+16}$$

Add -7 and 16 to get 9.

$$\frac{-\frac{32}{9}}{9}$$

Express \frac{-\frac{32}{9}}{9} as a single fraction.

$$\frac{-32}{9\times 9}$$

Multiply 9 and 9 to get 81.

$$\frac{-32}{81}$$

Fraction \frac{-32}{81} can be rewritten as -\frac{32}{81} by extracting the negative sign.

$$-\frac{32}{81}$$

Factor

$$-\frac{32}{81} = -0.3950617283950617$$