Solve -(-7/3)^-2-6/5(-10/21)+(-7)^2:(-7)^3=

$$- ( - \frac { 7 } { 3 } ) ^ { - 2 } - \frac { 6 } { 5 } ( - \frac { 10 } { 21 } ) + ( - 7 ) ^ { 2 } : ( - 7 ) ^ { 3 } =$$

Evaluate

$$\frac{12}{49}\approx 0.244897959$$

Solution Steps

Rewrite \left(-7\right)^{3} as -7\left(-7\right)^{2}. Cancel out \left(-7\right)^{2} in both numerator and denominator.

$$-\left(-\frac{7}{3}\right)^{-2}-\frac{6}{5}\left(-\frac{10}{21}\right)+\frac{1}{-7}$$

Calculate -\frac{7}{3} to the power of -2 and get \frac{9}{49}.

$$-\frac{9}{49}-\frac{6}{5}\left(-\frac{10}{21}\right)+\frac{1}{-7}$$

Multiply \frac{6}{5} and -\frac{10}{21} to get -\frac{4}{7}.

$$-\frac{9}{49}-\left(-\frac{4}{7}\right)+\frac{1}{-7}$$

The opposite of -\frac{4}{7} is \frac{4}{7}.

$$-\frac{9}{49}+\frac{4}{7}+\frac{1}{-7}$$

Add -\frac{9}{49} and \frac{4}{7} to get \frac{19}{49}.

$$\frac{19}{49}+\frac{1}{-7}$$

Fraction \frac{1}{-7} can be rewritten as -\frac{1}{7} by extracting the negative sign.

$$\frac{19}{49}-\frac{1}{7}$$

Subtract \frac{1}{7} from \frac{19}{49} to get \frac{12}{49}.

$$\frac{12}{49}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{7 ^ {2}} = 0.24489795918367346$$