Calculate (4/6)³: Solving a Cubed Fraction Expression

When you raise a fraction to a power, you're multiplying the entire fraction by itself that many times. So $\left(\frac{4}{6}\right)^3 = \frac{4}{6} \times \frac{4}{6} \times \frac{4}{6} = \frac{4^3}{6^3}$

$\left(\frac{4}{6}\right)^3 = \frac{4^3}{6^3} = \frac{64}{216}$, but $\frac{4^3}{6} = \frac{64}{6}$. The parentheses mean the exponent applies to the entire fraction!

You can do either! $\left(\frac{4}{2\times3}\right)^3 = \left(\frac{4}{6}\right)^3 = \frac{4^3}{6^3}$ or $\frac{4^3}{(2\times3)^3}$. Both are correct, but the second form matches the given expression exactly.

Look for the choice where both parts of the fraction are raised to the 3rd power. Only $\frac{4^3}{(2\times3)^3}$ shows this correctly - the others forgot to raise the denominator to the 3rd power.

Yes! $\frac{4^3}{(2\times3)^3} = \frac{64}{216} = \frac{8}{27}$ when simplified. But since the question asks for the expression, not the simplified form, keep it as $\frac{4^3}{(2\times3)^3}$.