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

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

Evaluate

$$-\frac{27}{32}=-0.84375$$

Solution Steps

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

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

Multiply \frac{1}{2} times \frac{81}{16} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 81}{2\times 16}.

$$\frac{81}{32}-\left(\frac{3}{2}\right)^{3}$$

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

$$\frac{81}{32}-\frac{27}{8}$$

Least common multiple of 32 and 8 is 32. Convert \frac{81}{32} and \frac{27}{8} to fractions with denominator 32.

$$\frac{81}{32}-\frac{108}{32}$$

Since \frac{81}{32} and \frac{108}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-108}{32}$$

Subtract 108 from 81 to get -27.

$$-\frac{27}{32}$$

Factor

$$-\frac{27}{32} = -0.84375$$