Solve 3{left(1/3right)}^4-4{left(1/3right)}^2+2

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

Evaluate

$$\frac{43}{27}\approx 1.592592593$$

Solution Steps

Calculate \frac{1}{3} to the power of 4 and get \frac{1}{81}.

$$3\times \frac{1}{81}-4\times \left(\frac{1}{3}\right)^{2}+2$$

Multiply 3 and \frac{1}{81} to get \frac{3}{81}.

$$\frac{3}{81}-4\times \left(\frac{1}{3}\right)^{2}+2$$

Reduce the fraction \frac{3}{81} to lowest terms by extracting and canceling out 3.

$$\frac{1}{27}-4\times \left(\frac{1}{3}\right)^{2}+2$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{1}{27}-4\times \frac{1}{9}+2$$

Multiply 4 and \frac{1}{9} to get \frac{4}{9}.

$$\frac{1}{27}-\frac{4}{9}+2$$

Least common multiple of 27 and 9 is 27. Convert \frac{1}{27} and \frac{4}{9} to fractions with denominator 27.

$$\frac{1}{27}-\frac{12}{27}+2$$

Since \frac{1}{27} and \frac{12}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-12}{27}+2$$

Subtract 12 from 1 to get -11.

$$-\frac{11}{27}+2$$

Convert 2 to fraction \frac{54}{27}.

$$-\frac{11}{27}+\frac{54}{27}$$

Since -\frac{11}{27} and \frac{54}{27} have the same denominator, add them by adding their numerators.

$$\frac{-11+54}{27}$$

Add -11 and 54 to get 43.

$$\frac{43}{27}$$

Factor

$$\frac{43}{3 ^ {3}} = 1\frac{16}{27} = 1.5925925925925926$$