Calculate (1/3)³: Solving the Cube of One-Third

When you cube a fraction less than 1, like $\frac{1}{3}$, you're multiplying it by itself three times. Since you're multiplying by numbers less than 1, the result gets smaller: $\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$.

That's completely different! $\frac{1^3}{3} = \frac{1}{3}$ means only the numerator is cubed. But $(\frac{1}{3})^3$ means the entire fraction is cubed, so both parts get the exponent: $\frac{1^3}{3^3}$.

Absolutely! That's exactly what cubing means. Multiply the numerators: $1 \times 1 \times 1 = 1$, and multiply the denominators: $3 \times 3 \times 3 = 27$ to get $\frac{1}{27}$.

The same rule applies! For example, $(\frac{2}{5})^3 = \frac{2^3}{5^3} = \frac{8}{125}$. Always cube both the top and bottom numbers separately.

Think of it as distributing the exponent: the exponent outside the parentheses applies to everything inside. Just like $(ab)^3 = a^3b^3$, we have $(\frac{a}{b})^3 = \frac{a^3}{b^3}$!