Solve 12{left(-2/3right)}^3-13{left(-2/3right)}^2-5(-2/3)+7=

$$12 { \left( \frac{ -2 }{ 3 } \right) }^{ 3 } -13 { \left( \frac{ -2 }{ 3 } \right) }^{ 2 } -5( \frac{ -2 }{ 3 } )+7=$$

Evaluate

$$1$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$12\left(-\frac{2}{3}\right)^{3}-13\times \left(\frac{-2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$12\left(-\frac{8}{27}\right)-13\times \left(\frac{-2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Multiply 12 and -\frac{8}{27} to get -\frac{32}{9}.

$$-\frac{32}{9}-13\times \left(\frac{-2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{32}{9}-13\left(-\frac{2}{3}\right)^{2}-5\times \frac{-2}{3}+7$$

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

$$-\frac{32}{9}-13\times \frac{4}{9}-5\times \frac{-2}{3}+7$$

Multiply 13 and \frac{4}{9} to get \frac{52}{9}.

$$-\frac{32}{9}-\frac{52}{9}-5\times \frac{-2}{3}+7$$

Subtract \frac{52}{9} from -\frac{32}{9} to get -\frac{28}{3}.

$$-\frac{28}{3}-5\times \frac{-2}{3}+7$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$-\frac{28}{3}-5\left(-\frac{2}{3}\right)+7$$

Multiply 5 and -\frac{2}{3} to get -\frac{10}{3}.

$$-\frac{28}{3}-\left(-\frac{10}{3}\right)+7$$

The opposite of -\frac{10}{3} is \frac{10}{3}.

$$-\frac{28}{3}+\frac{10}{3}+7$$

Add -\frac{28}{3} and \frac{10}{3} to get -6.

$$-6+7$$

Add -6 and 7 to get 1.

$$1$$

Factor

$$1$$