Solve (+2/3)^2*(+2/3)^3:(+2/3)+(-1)^4*(-1)^3+11/9-frac{7}{9}=

$$( + \frac { 2 } { 3 } ) ^ { 2 } \cdot ( + \frac { 2 } { 3 } ) ^ { 3 } : ( + \frac { 2 } { 3 } ) + ( - 1 ) ^ { 4 } \cdot ( - 1 ) ^ { 3 } + \frac { 11 } { 9 } - \frac { 7 } { 9 } =$$

Evaluate

$$-\frac{29}{81}\approx -0.358024691$$

Solution Steps

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

$$\frac{\left(\frac{2}{3}\right)^{5}}{\frac{2}{3}}+\left(-1\right)^{4}\left(-1\right)^{3}+\frac{11}{9}-\frac{7}{9}$$

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

$$\left(\frac{2}{3}\right)^{4}+\left(-1\right)^{4}\left(-1\right)^{3}+\frac{11}{9}-\frac{7}{9}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\left(\frac{2}{3}\right)^{4}+\left(-1\right)^{7}+\frac{11}{9}-\frac{7}{9}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{16}{81}+\left(-1\right)^{7}+\frac{11}{9}-\frac{7}{9}$$

Calculate -1 to the power of 7 and get -1.

$$\frac{16}{81}-1+\frac{11}{9}-\frac{7}{9}$$

Convert 1 to fraction \frac{81}{81}.

$$\frac{16}{81}-\frac{81}{81}+\frac{11}{9}-\frac{7}{9}$$

Since \frac{16}{81} and \frac{81}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-81}{81}+\frac{11}{9}-\frac{7}{9}$$

Subtract 81 from 16 to get -65.

$$-\frac{65}{81}+\frac{11}{9}-\frac{7}{9}$$

Least common multiple of 81 and 9 is 81. Convert -\frac{65}{81} and \frac{11}{9} to fractions with denominator 81.

$$-\frac{65}{81}+\frac{99}{81}-\frac{7}{9}$$

Since -\frac{65}{81} and \frac{99}{81} have the same denominator, add them by adding their numerators.

$$\frac{-65+99}{81}-\frac{7}{9}$$

Add -65 and 99 to get 34.

$$\frac{34}{81}-\frac{7}{9}$$

Least common multiple of 81 and 9 is 81. Convert \frac{34}{81} and \frac{7}{9} to fractions with denominator 81.

$$\frac{34}{81}-\frac{63}{81}$$

Since \frac{34}{81} and \frac{63}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-63}{81}$$

Subtract 63 from 34 to get -29.

$$-\frac{29}{81}$$

Factor

$$-\frac{29}{81} = -0.35802469135802467$$