Solve f(2)=-1/9*2^3+2/3*2^2+3

$$f ( 2 ) = - \frac { 1 } { 9 } \cdot 2 ^ { 3 } + \frac { 2 } { 3 } \cdot 2 ^ { 2 } + 3$$

Evaluate

$$\frac{43}{9}\approx 4.777777778$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$-\frac{1}{9}\times 8+\frac{2}{3}\times 2^{2}+3$$

Express -\frac{1}{9}\times 8 as a single fraction.

$$\frac{-8}{9}+\frac{2}{3}\times 2^{2}+3$$

Fraction \frac{-8}{9} can be rewritten as -\frac{8}{9} by extracting the negative sign.

$$-\frac{8}{9}+\frac{2}{3}\times 2^{2}+3$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{8}{9}+\frac{2}{3}\times 4+3$$

Express \frac{2}{3}\times 4 as a single fraction.

$$-\frac{8}{9}+\frac{2\times 4}{3}+3$$

Multiply 2 and 4 to get 8.

$$-\frac{8}{9}+\frac{8}{3}+3$$

Least common multiple of 9 and 3 is 9. Convert -\frac{8}{9} and \frac{8}{3} to fractions with denominator 9.

$$-\frac{8}{9}+\frac{24}{9}+3$$

Since -\frac{8}{9} and \frac{24}{9} have the same denominator, add them by adding their numerators.

$$\frac{-8+24}{9}+3$$

Add -8 and 24 to get 16.

$$\frac{16}{9}+3$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{16}{9}+\frac{27}{9}$$

Since \frac{16}{9} and \frac{27}{9} have the same denominator, add them by adding their numerators.

$$\frac{16+27}{9}$$

Add 16 and 27 to get 43.

$$\frac{43}{9}$$

Factor

$$\frac{43}{3 ^ {2}} = 4\frac{7}{9} = 4.777777777777778$$