Solve (3/2)^4-2*(3/2)^3

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

Evaluate

$$-\frac{27}{16}=-1.6875$$

Solution Steps

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

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

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

$$\frac{81}{16}-2\times \frac{27}{8}$$

Express 2\times \frac{27}{8} as a single fraction.

$$\frac{81}{16}-\frac{2\times 27}{8}$$

Multiply 2 and 27 to get 54.

$$\frac{81}{16}-\frac{54}{8}$$

Reduce the fraction \frac{54}{8} to lowest terms by extracting and canceling out 2.

$$\frac{81}{16}-\frac{27}{4}$$

Least common multiple of 16 and 4 is 16. Convert \frac{81}{16} and \frac{27}{4} to fractions with denominator 16.

$$\frac{81}{16}-\frac{108}{16}$$

Since \frac{81}{16} and \frac{108}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-108}{16}$$

Subtract 108 from 81 to get -27.

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

Factor

$$-\frac{27}{16} = -1\frac{11}{16} = -1.6875$$