Solve -1/3*2/3-2/3*(-1/3)*(frac{2}{3})^2-frac{2}{9}*(frac{2}{3})^3

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

Evaluate

$$-\frac{46}{243}\approx -0.189300412$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply -\frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-2}{3\times 3}.

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

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

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

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

$$-\frac{2}{9}-\frac{8}{27}\left(-\frac{1}{3}\right)-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

Multiply \frac{8}{27} times -\frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{2}{9}-\frac{8\left(-1\right)}{27\times 3}-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

Do the multiplications in the fraction \frac{8\left(-1\right)}{27\times 3}.

$$-\frac{2}{9}-\frac{-8}{81}-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

Fraction \frac{-8}{81} can be rewritten as -\frac{8}{81} by extracting the negative sign.

$$-\frac{2}{9}-\left(-\frac{8}{81}\right)-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

The opposite of -\frac{8}{81} is \frac{8}{81}.

$$-\frac{2}{9}+\frac{8}{81}-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

Least common multiple of 9 and 81 is 81. Convert -\frac{2}{9} and \frac{8}{81} to fractions with denominator 81.

$$-\frac{18}{81}+\frac{8}{81}-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

Since -\frac{18}{81} and \frac{8}{81} have the same denominator, add them by adding their numerators.

$$\frac{-18+8}{81}-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

Add -18 and 8 to get -10.

$$-\frac{10}{81}-\frac{2}{9}\times \left(\frac{2}{3}\right)^{3}$$

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

$$-\frac{10}{81}-\frac{2}{9}\times \frac{8}{27}$$

Multiply \frac{2}{9} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{10}{81}-\frac{2\times 8}{9\times 27}$$

Do the multiplications in the fraction \frac{2\times 8}{9\times 27}.

$$-\frac{10}{81}-\frac{16}{243}$$

Least common multiple of 81 and 243 is 243. Convert -\frac{10}{81} and \frac{16}{243} to fractions with denominator 243.

$$-\frac{30}{243}-\frac{16}{243}$$

Since -\frac{30}{243} and \frac{16}{243} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-30-16}{243}$$

Subtract 16 from -30 to get -46.

$$-\frac{46}{243}$$

Factor

$$-\frac{46}{243} = -0.18930041152263374$$