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We are given the equation \( a^3 = b^2 \) and asked to find which of the given options equals \( b\sqrt{a} \).

### Step 1: Express \( a \) in terms of \( b \)
From the equation \( a^3 = b^2 \), we can solve for \( a \) by taking the cube root of both sides:
\[
a = (b^2)^{1/3} = b^{2/3}
\]

### Step 2: Substitute \( a \) into the expression \( b\sqrt{a} \)
We now substitute \( a = b^{2/3} \) into the expression \( b\sqrt{a} \). The square root of \( a \) is:
\[
\sqrt{a} = \sqrt{b^{2/3}} = b^{(2/3) \cdot (1/2)} = b^{1/3}
\]

Thus, the expression \( b\sqrt{a} \) becomes:
\[
b\sqrt{a} = b \cdot b^{1/3} = b^{1 + 1/3} = b^{4/3}
\]

### Conclusion:
The correct answer is **B) \( b^{4/3} \)**.

Would you like further explanation or details on any step? Here are some related questions you can explore:

1. How do you simplify expressions with fractional exponents?
2. What are the properties of cube roots and square roots?
3. How do you combine terms with the same base in exponentiation?
4. Can you generalize this method for any similar equation?
5. What happens if \( a^n = b^m \) and you need to find a similar expression?

**Tip:** When dealing with exponents and radicals, always rewrite the roots as fractional exponents for easier simplification.

If a^3 = b^2, which of the following is equal to b√a?

Find the value of b√a given that a^3 = b^2. This algebra problem explores exponentiation and radical simplification using key exponent laws, suitable for students in Grades 10-12.

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