Solve 3{left(3/2right)}^3-4{left(3/2right)}^+5

$$3 { \left( \frac{ 3 }{ 2 } \right) }^{ 3 } -4 { \left( \frac{ 3 }{ 2 } \right) }^{ } +5$$

Evaluate

$$\frac{73}{8}=9.125$$

Solution Steps

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

$$3\times \frac{27}{8}-4\times \left(\frac{3}{2}\right)^{1}+5$$

Express 3\times \frac{27}{8} as a single fraction.

$$\frac{3\times 27}{8}-4\times \left(\frac{3}{2}\right)^{1}+5$$

Multiply 3 and 27 to get 81.

$$\frac{81}{8}-4\times \left(\frac{3}{2}\right)^{1}+5$$

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

$$\frac{81}{8}-4\times \frac{3}{2}+5$$

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

$$\frac{81}{8}-\frac{4\times 3}{2}+5$$

Multiply 4 and 3 to get 12.

$$\frac{81}{8}-\frac{12}{2}+5$$

Divide 12 by 2 to get 6.

$$\frac{81}{8}-6+5$$

Convert 6 to fraction \frac{48}{8}.

$$\frac{81}{8}-\frac{48}{8}+5$$

Since \frac{81}{8} and \frac{48}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81-48}{8}+5$$

Subtract 48 from 81 to get 33.

$$\frac{33}{8}+5$$

Convert 5 to fraction \frac{40}{8}.

$$\frac{33}{8}+\frac{40}{8}$$

Since \frac{33}{8} and \frac{40}{8} have the same denominator, add them by adding their numerators.

$$\frac{33+40}{8}$$

Add 33 and 40 to get 73.

$$\frac{73}{8}$$

Factor

$$\frac{73}{2 ^ {3}} = 9\frac{1}{8} = 9.125$$