Solve 292[(-7/3)^{-2}]^-2*(7/3)^-3:(-7/3)^5+(-49/9)^-2

$$292 [ ( - \frac { 7 } { 3 } ) ^ { - 2 } ] ^ { - 2 } \cdot ( \frac { 7 } { 3 } ) ^ { - 3 } : ( - \frac { 7 } { 3 } ) ^ { 5 } + ( - \frac { 49 } { 9 } ) ^ { - 2 }$$

Evaluate

$$-\frac{23571}{2401}\approx -9.817159517$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -2 and -2 to get 4.

$$\frac{292\left(-\frac{7}{3}\right)^{4}\times \left(\frac{7}{3}\right)^{-3}}{\left(-\frac{7}{3}\right)^{5}}+\left(-\frac{49}{9}\right)^{-2}$$

Cancel out \left(-\frac{7}{3}\right)^{4} in both numerator and denominator.

$$\frac{292\times \left(\frac{7}{3}\right)^{-3}}{-\frac{7}{3}}+\left(-\frac{49}{9}\right)^{-2}$$

Calculate \frac{7}{3} to the power of -3 and get \frac{27}{343}.

$$\frac{292\times \frac{27}{343}}{-\frac{7}{3}}+\left(-\frac{49}{9}\right)^{-2}$$

Multiply 292 and \frac{27}{343} to get \frac{7884}{343}.

$$\frac{\frac{7884}{343}}{-\frac{7}{3}}+\left(-\frac{49}{9}\right)^{-2}$$

Divide \frac{7884}{343} by -\frac{7}{3} by multiplying \frac{7884}{343} by the reciprocal of -\frac{7}{3}.

$$\frac{7884}{343}\left(-\frac{3}{7}\right)+\left(-\frac{49}{9}\right)^{-2}$$

Multiply \frac{7884}{343} and -\frac{3}{7} to get -\frac{23652}{2401}.

$$-\frac{23652}{2401}+\left(-\frac{49}{9}\right)^{-2}$$

Calculate -\frac{49}{9} to the power of -2 and get \frac{81}{2401}.

$$-\frac{23652}{2401}+\frac{81}{2401}$$

Add -\frac{23652}{2401} and \frac{81}{2401} to get -\frac{23571}{2401}.

$$-\frac{23571}{2401}$$

Factor

$$-\frac{23571}{2401} = -9\frac{1962}{2401} = -9.81715951686797$$