TAOCP 1.2.2 Exercise 3

By Eq.

taocpmathematicsalgorithmsvolume-1simple

Section 1.2.2: Numbers, Powers, and Logarithms

Exercise 3. [02] What is $(-3)^{-3}$?

Verified: yes
Solve time: 31s

By Eq. (4),

$(-3)^{-3} = \frac{(-3)^{-2}}{-3} = \frac{(-3)^{-1}}{(-3)^2} = \frac{1}{(-3)^3}.$

Since

$(-3)^3 = (-3)(-3)(-3) = 9(-3) = -27,$

we obtain

$(-3)^{-3} = \frac{1}{-27} = -\frac{1}{27}.$

Therefore the answer is

$\boxed{-\frac{1}{27}}.$