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The problem provided asks us to solve for \( u \) in the equation:

\[
u^{\frac{1}{3}} = 216
\]

To eliminate the fractional exponent, we can cube both sides of the equation:

\[
\left( u^{\frac{1}{3}} \right)^3 = 216^3
\]

This simplifies to:

\[
u = 216^3
\]

Now, we calculate \( 216^3 \):

\[
216^3 = 216 \times 216 \times 216 = 10077696
\]

Thus, the solution is:

\[
u = 10077696
\]

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would you solve \( u^{\frac{1}{4}} = 81 \) for \( u \)?
2. What happens if the exponent is a negative fraction, such as \( u^{-\frac{1}{3}} = 216 \)?
3. How would you solve an equation like \( u^{\frac{1}{3}} = -216 \)?
4. What is the general approach for solving equations of the form \( u^{\frac{1}{n}} = a \)?
5. Can you rewrite fractional exponents as roots and solve using square or cube roots?

**Tip:** When working with fractional exponents, remember that \( x^{\frac{1}{n}} \) represents the \( n \)-th root of \( x \).

Solve u^(1/3) = 216, where u is a real number. Simplify your answer as much as possible.

Learn how to solve the equation u^(1/3) = 216 with a step-by-step solution. This problem covers algebraic concepts related to exponents and roots, providing a simplified answer. Suitable for students in Grades 9-11.

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