Solve (4.5-3)(4.5-4)(4.5-5)(4.5-6)*(-6)*(4.5)^-4/4!

$$\frac { ( 4.5 - 3 ) ( 4.5 - 4 ) ( 4.5 - 5 ) ( 4.5 - 6 ) \times ( - 6 ) \times ( 4.5 ) ^ { - 4 } } { 4 ! }$$

Evaluate

$$-\frac{1}{2916}\approx -0.000342936$$

Solution Steps

Subtract 3 from 4.5 to get 1.5.

$$\frac{1.5\left(4.5-4\right)\left(4.5-5\right)\left(4.5-6\right)\left(-6\right)\times 4.5^{-4}}{4!}$$

Subtract 4 from 4.5 to get 0.5.

$$\frac{1.5\times 0.5\left(4.5-5\right)\left(4.5-6\right)\left(-6\right)\times 4.5^{-4}}{4!}$$

Multiply 1.5 and 0.5 to get 0.75.

$$\frac{0.75\left(4.5-5\right)\left(4.5-6\right)\left(-6\right)\times 4.5^{-4}}{4!}$$

Subtract 5 from 4.5 to get -0.5.

$$\frac{0.75\left(-0.5\right)\left(4.5-6\right)\left(-6\right)\times 4.5^{-4}}{4!}$$

Multiply 0.75 and -0.5 to get -0.375.

$$\frac{-0.375\left(4.5-6\right)\left(-6\right)\times 4.5^{-4}}{4!}$$

Subtract 6 from 4.5 to get -1.5.

$$\frac{-0.375\left(-1.5\right)\left(-6\right)\times 4.5^{-4}}{4!}$$

Multiply -0.375 and -1.5 to get 0.5625.

$$\frac{0.5625\left(-6\right)\times 4.5^{-4}}{4!}$$

Multiply 0.5625 and -6 to get -3.375.

$$\frac{-3.375\times 4.5^{-4}}{4!}$$

Calculate 4.5 to the power of -4 and get \frac{16}{6561}.

$$\frac{-3.375\times \frac{16}{6561}}{4!}$$

Multiply -3.375 and \frac{16}{6561} to get -\frac{2}{243}.

$$\frac{-\frac{2}{243}}{4!}$$

The factorial of 4 is 24.

$$\frac{-\frac{2}{243}}{24}$$

Factor

$$-\frac{1}{2916} = -0.0003429355281207133$$