Solve 5/4*(-2/3)-(-2/3)^3*(-2/3)^2:(-frac{2}{3})^4

$$\frac { 5 } { 4 } \cdot ( - \frac { 2 } { 3 } ) - ( - \frac { 2 } { 3 } ) ^ { 3 } \cdot ( - \frac { 2 } { 3 } ) ^ { 2 } : ( - \frac { 2 } { 3 } ) ^ { 4 }$$

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{5}{4}\left(-\frac{2}{3}\right)-\frac{\left(-\frac{2}{3}\right)^{5}}{\left(-\frac{2}{3}\right)^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\frac{5}{4}\left(-\frac{2}{3}\right)-\left(-\frac{2}{3}\right)^{1}$$

Multiply \frac{5}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-2\right)}{4\times 3}-\left(-\frac{2}{3}\right)^{1}$$

Do the multiplications in the fraction \frac{5\left(-2\right)}{4\times 3}.

$$\frac{-10}{12}-\left(-\frac{2}{3}\right)^{1}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

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

Calculate -\frac{2}{3} to the power of 1 and get -\frac{2}{3}.

$$-\frac{5}{6}-\left(-\frac{2}{3}\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$-\frac{5}{6}+\frac{2}{3}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

$$-\frac{5}{6}+\frac{4}{6}$$

Since -\frac{5}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{-5+4}{6}$$

Add -5 and 4 to get -1.

$$-\frac{1}{6}$$

Factor

$$-\frac{1}{6} = -0.16666666666666666$$