Calculate (3/4)³: Solving the Cube of Three-Fourths

Because $(\frac{3}{4})^3$ means multiply the entire fraction by itself three times: $\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4}$. This gives you $\frac{3 \times 3 \times 3}{4 \times 4 \times 4}$.

Big difference! $(\frac{3}{4})^3 = \frac{27}{64}$ means the whole fraction is cubed, while $\frac{3}{4^3} = \frac{3}{64}$ means only the denominator is cubed.

Check if the numerator and denominator share any common factors. Since 27 = 3³ and 64 = 4³ = 2⁶, they share no common factors, so $\frac{27}{64}$ is already fully simplified.

Yes! $\frac{27}{64} = 0.421875$ exactly. But for most math problems, leaving the answer as a simplified fraction is preferred and more precise.

A negative exponent means flip and make positive: $(\frac{3}{4})^{-3} = (\frac{4}{3})^3 = \frac{64}{27}$. It's the reciprocal of the positive power!