Solve -(-2)^3div17/9*(-4/3)^2

$$- ( - 2 ) ^ { 3 } \div 1 \frac { 7 } { 9 } \times ( - \frac { 4 } { 3 } ) ^ { 2 }$$

Evaluate

$$8$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$\frac{-\left(-8\right)}{\frac{1\times 9+7}{9}}\left(-\frac{4}{3}\right)^{2}$$

The opposite of -8 is 8.

$$\frac{8}{\frac{1\times 9+7}{9}}\left(-\frac{4}{3}\right)^{2}$$

Multiply 1 and 9 to get 9.

$$\frac{8}{\frac{9+7}{9}}\left(-\frac{4}{3}\right)^{2}$$

Add 9 and 7 to get 16.

$$\frac{8}{\frac{16}{9}}\left(-\frac{4}{3}\right)^{2}$$

Divide 8 by \frac{16}{9} by multiplying 8 by the reciprocal of \frac{16}{9}.

$$8\times \frac{9}{16}\left(-\frac{4}{3}\right)^{2}$$

Express 8\times \frac{9}{16} as a single fraction.

$$\frac{8\times 9}{16}\left(-\frac{4}{3}\right)^{2}$$

Multiply 8 and 9 to get 72.

$$\frac{72}{16}\left(-\frac{4}{3}\right)^{2}$$

Reduce the fraction \frac{72}{16} to lowest terms by extracting and canceling out 8.

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

Calculate -\frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{9}{2}\times \frac{16}{9}$$

Multiply \frac{9}{2} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 16}{2\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{16}{2}$$

Divide 16 by 2 to get 8.

$$8$$

Factor

$$2^{3}$$