Solve 3(2/3)^4-4(2/3)^3+1

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

Evaluate

$$\frac{11}{27}\approx 0.407407407$$

Solution Steps

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

$$3\times \frac{16}{81}-4\times \left(\frac{2}{3}\right)^{3}+1$$

Express 3\times \frac{16}{81} as a single fraction.

$$\frac{3\times 16}{81}-4\times \left(\frac{2}{3}\right)^{3}+1$$

Multiply 3 and 16 to get 48.

$$\frac{48}{81}-4\times \left(\frac{2}{3}\right)^{3}+1$$

Reduce the fraction \frac{48}{81} to lowest terms by extracting and canceling out 3.

$$\frac{16}{27}-4\times \left(\frac{2}{3}\right)^{3}+1$$

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

$$\frac{16}{27}-4\times \frac{8}{27}+1$$

Express 4\times \frac{8}{27} as a single fraction.

$$\frac{16}{27}-\frac{4\times 8}{27}+1$$

Multiply 4 and 8 to get 32.

$$\frac{16}{27}-\frac{32}{27}+1$$

Since \frac{16}{27} and \frac{32}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-32}{27}+1$$

Subtract 32 from 16 to get -16.

$$-\frac{16}{27}+1$$

Convert 1 to fraction \frac{27}{27}.

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

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

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

Add -16 and 27 to get 11.

$$\frac{11}{27}$$

Factor

$$\frac{11}{3 ^ {3}} = 0.4074074074074074$$