Solve (6/11)^5*(-11/6)^7*(-6/11)^3

$$( \frac { 6 } { 11 } ) ^ { 5 } \cdot ( - \frac { 11 } { 6 } ) ^ { 7 } \cdot ( - \frac { 6 } { 11 } ) ^ { 3 }$$

Evaluate

$$\frac{6}{11}\approx 0.545454545$$

Solution Steps

Calculate \frac{6}{11} to the power of 5 and get \frac{7776}{161051}.

$$\frac{7776}{161051}\left(-\frac{11}{6}\right)^{7}\left(-\frac{6}{11}\right)^{3}$$

Calculate -\frac{11}{6} to the power of 7 and get -\frac{19487171}{279936}.

$$\frac{7776}{161051}\left(-\frac{19487171}{279936}\right)\left(-\frac{6}{11}\right)^{3}$$

Multiply \frac{7776}{161051} times -\frac{19487171}{279936} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7776\left(-19487171\right)}{161051\times 279936}\left(-\frac{6}{11}\right)^{3}$$

Do the multiplications in the fraction \frac{7776\left(-19487171\right)}{161051\times 279936}.

$$\frac{-151532241696}{45083972736}\left(-\frac{6}{11}\right)^{3}$$

Reduce the fraction \frac{-151532241696}{45083972736} to lowest terms by extracting and canceling out 1252332576.

$$-\frac{121}{36}\left(-\frac{6}{11}\right)^{3}$$

Calculate -\frac{6}{11} to the power of 3 and get -\frac{216}{1331}.

$$-\frac{121}{36}\left(-\frac{216}{1331}\right)$$

Multiply -\frac{121}{36} times -\frac{216}{1331} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-121\left(-216\right)}{36\times 1331}$$

Do the multiplications in the fraction \frac{-121\left(-216\right)}{36\times 1331}.

$$\frac{26136}{47916}$$

Reduce the fraction \frac{26136}{47916} to lowest terms by extracting and canceling out 4356.

$$\frac{6}{11}$$

Factor

$$\frac{2 \cdot 3}{11} = 0.5454545454545454$$