Multiply Fourth and Seventh Roots: Solving ⁴√8 · ⁷√8

Because roots don't multiply that way! Root multiplication requires converting to exponents first. Think of it like this: $\sqrt[4]{8}$ means "what number raised to the 4th power gives 8?" You need exponent laws, not simple multiplication.

Remember: when you multiply same bases, you add the exponents. Since both terms have base 8, we add $\frac{1}{4} + \frac{1}{7}$. If the bases were different, you couldn't combine them this way!

No! Leave your answer as $8^{\frac{1}{4}+\frac{1}{7}}$. This exact form shows you understand the exponent laws. Converting to decimals often creates rounding errors and loses the mathematical precision.

If you had something like $\sqrt[4]{8} \cdot \sqrt[7]{16}$, you cannot combine them using the same base rule. You'd need to convert both to the same base first (like powers of 2) or calculate each root separately.

You could find a common denominator for $\frac{1}{4} + \frac{1}{7} = \frac{7+4}{28} = \frac{11}{28}$, but it's not required. The answer $8^{\frac{1}{4}+\frac{1}{7}}$ clearly shows your work and is perfectly acceptable!