Calculate 1/12³: Solving a Cube Fraction Problem

A negative exponent means "take the reciprocal and use the positive exponent." So $12^{-3} = \frac{1}{12^3}$. It's like flipping the fraction!

This is the negative exponent rule! When you have $a^{-n}$, it equals $\frac{1}{a^n}$. They're just two different ways to write the same mathematical value.

$12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728$. So $\frac{1}{12^3} = \frac{1}{1728}$, which confirms our answer!

It's positive! The negative sign in the exponent doesn't make the result negative. $12^{-3} = \frac{1}{1728}$ is a small positive fraction.

Both $12^{-3}$ and $\frac{1}{1728}$ are correct! However, $12^{-3}$ is often preferred because it shows the relationship to the original expression more clearly.