Solve frac{[(2/3)^{-1}]^{0}-[(2/3)^{2}]^{-1}}{[(1/3)^2]^-1+[(1/3)^-1]^2}

$$\frac { [ ( 2 / 3 ) ^ { - 1 } ] ^ { 0 } - [ ( 2 / 3 ) ^ { 2 } ] ^ { - 1 } } { [ ( 1 / 3 ) ^ { 2 } ] ^ { - 1 } + [ ( 1 / 3 ) ^ { - 1 } ] ^ { 2 } }$$

Evaluate

$$-\frac{5}{72}\approx -0.069444444$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -1 and 0 to get 0.

$$\frac{\left(\frac{2}{3}\right)^{0}-\left(\left(\frac{2}{3}\right)^{2}\right)^{-1}}{\left(\left(\frac{1}{3}\right)^{2}\right)^{-1}+\left(\left(\frac{1}{3}\right)^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(\frac{2}{3}\right)^{0}-\left(\frac{2}{3}\right)^{-2}}{\left(\left(\frac{1}{3}\right)^{2}\right)^{-1}+\left(\left(\frac{1}{3}\right)^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(\frac{2}{3}\right)^{0}-\left(\frac{2}{3}\right)^{-2}}{\left(\frac{1}{3}\right)^{-2}+\left(\left(\frac{1}{3}\right)^{-1}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{\left(\frac{2}{3}\right)^{0}-\left(\frac{2}{3}\right)^{-2}}{\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}}$$

Calculate \frac{2}{3} to the power of 0 and get 1.

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

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

$$\frac{1-\frac{9}{4}}{\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}}$$

Subtract \frac{9}{4} from 1 to get -\frac{5}{4}.

$$\frac{-\frac{5}{4}}{\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}}$$

Calculate \frac{1}{3} to the power of -2 and get 9.

$$\frac{-\frac{5}{4}}{9+\left(\frac{1}{3}\right)^{-2}}$$

Calculate \frac{1}{3} to the power of -2 and get 9.

$$\frac{-\frac{5}{4}}{9+9}$$

Add 9 and 9 to get 18.

$$\frac{-\frac{5}{4}}{18}$$

Express \frac{-\frac{5}{4}}{18} as a single fraction.

$$\frac{-5}{4\times 18}$$

Multiply 4 and 18 to get 72.

$$\frac{-5}{72}$$

Fraction \frac{-5}{72} can be rewritten as -\frac{5}{72} by extracting the negative sign.

$$-\frac{5}{72}$$

Factor

$$-\frac{5}{72} = -0.06944444444444445$$