Solve Fourth and Sixth Roots: Multiplying √⁴3 × √⁶3

Because radical indices don't add directly! You must first convert to exponential form: $\sqrt[4]{3} = 3^{\frac{1}{4}}$ and $\sqrt[6]{3} = 3^{\frac{1}{6}}$, then add the exponents.

No! The exact form $3^{\frac{1}{4}+\frac{1}{6}}$ is the most precise answer. Converting to decimals would introduce rounding errors and lose mathematical accuracy.

If the bases were different (like $\sqrt[4]{3} \cdot \sqrt[6]{5}$), you cannot combine them using exponent rules. The multiplication rule only works when the bases are identical.

Find the LCD (Least Common Denominator): LCD of 4 and 6 is 12. Convert: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{6} = \frac{2}{12}$, so $\frac{1}{4} + \frac{1}{6} = \frac{5}{12}$.

Yes! Both $3^{\frac{1}{4}+\frac{1}{6}}$ and $3^{\frac{5}{12}}$ are correct. The first form clearly shows the work, while the second is more simplified.