Given the equation $a^{1/3} = \frac{w}{b^{1/3}}$, we want to solve for $a$.

Step 1: Isolate $a^{1/3}$

The equation is already isolated with respect to $a^{1/3}$: $a^{1/3} = \frac{w}{b^{1/3}}$

Step 2: Cube both sides of the equation

To solve for $a$, we cube both sides of the equation to eliminate the cube root: $(a^{1/3})^3 = \left(\frac{w}{b^{1/3}}\right)^3$

This simplifies to: $a = \frac{w^3}{b}$

Final Answer:

$a = \frac{w^3}{b}$

Would you like more details or have any questions?

Here are 8 related questions you might be interested in:

1. What is the general method for solving radical equations?
2. How do you simplify fractional exponents?
3. What are the rules for exponentiation when dealing with roots?
4. Can you solve an equation involving different roots, such as square and cube roots?
5. How does exponentiation relate to logarithms?
6. What is the cube root of a negative number?
7. How do you solve for a variable in a fractional equation?
8. How do you apply the power of a quotient rule in algebra?

Tip: When dealing with fractional exponents, remember that the exponent's numerator indicates the power, while the denominator indicates the root.