Solve ((2/3)^2)*(2/3)^2+(2/3)^2quad2

$$( ( \frac { 2 } { 3 } ) ^ { 2 } ) \times ( \frac { 2 } { 3 } ) ^ { 2 } + ( \frac { 2 } { 3 } ) ^ { 2 } \quad 2$$

Evaluate

$$\frac{88}{81}\approx 1.086419753$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\left(\frac{2}{3}\right)^{4}+\left(\frac{2}{3}\right)^{2}\times 2$$

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

$$\frac{16}{81}+\left(\frac{2}{3}\right)^{2}\times 2$$

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

$$\frac{16}{81}+\frac{4}{9}\times 2$$

Express \frac{4}{9}\times 2 as a single fraction.

$$\frac{16}{81}+\frac{4\times 2}{9}$$

Multiply 4 and 2 to get 8.

$$\frac{16}{81}+\frac{8}{9}$$

Least common multiple of 81 and 9 is 81. Convert \frac{16}{81} and \frac{8}{9} to fractions with denominator 81.

$$\frac{16}{81}+\frac{72}{81}$$

Since \frac{16}{81} and \frac{72}{81} have the same denominator, add them by adding their numerators.

$$\frac{16+72}{81}$$

Add 16 and 72 to get 88.

$$\frac{88}{81}$$

Factor

$$\frac{2 ^ {3} \cdot 11}{3 ^ {4}} = 1\frac{7}{81} = 1.0864197530864197$$