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The problem you uploaded asks to simplify the following expression:

\[
\left(\frac{a^{\frac{2}{3}}}{b^{\frac{1}{2}}}\right)^{-1} \times \frac{(a^{\frac{2}{3}} b^{\frac{1}{2}})^2 \times a^{\frac{1}{3}}}{b^{\frac{1}{2}}}
\]

### Step 1: Simplify \(\left(\frac{a^{\frac{2}{3}}}{b^{\frac{1}{2}}}\right)^{-1}\)

When you take the inverse (raise to the power of \(-1\)), you flip the fraction:

\[
\left(\frac{a^{\frac{2}{3}}}{b^{\frac{1}{2}}}\right)^{-1} = \frac{b^{\frac{1}{2}}}{a^{\frac{2}{3}}}
\]

### Step 2: Simplify the second part \(\frac{(a^{\frac{2}{3}} b^{\frac{1}{2}})^2 \times a^{\frac{1}{3}}}{b^{\frac{1}{2}}}\)

First, apply the power of 2 to both \(a^{\frac{2}{3}}\) and \(b^{\frac{1}{2}}\):

\[
(a^{\frac{2}{3}} b^{\frac{1}{2}})^2 = a^{\frac{4}{3}} b^1
\]

Now, multiply by \(a^{\frac{1}{3}}\):

\[
a^{\frac{4}{3}} \times a^{\frac{1}{3}} = a^{\frac{5}{3}}
\]

So the expression becomes:

\[
\frac{a^{\frac{5}{3}} b^1}{b^{\frac{1}{2}}} = a^{\frac{5}{3}} b^{\frac{1}{2}}
\]

### Step 3: Combine both parts

Now, multiply the two simplified expressions:

\[
\frac{b^{\frac{1}{2}}}{a^{\frac{2}{3}}} \times a^{\frac{5}{3}} b^{\frac{1}{2}} = \frac{a^{\frac{5}{3}}}{a^{\frac{2}{3}}} \times \frac{b^{\frac{1}{2}}}{1} = a^1 b^1 = ab
\]

### Final Answer: \( \boxed{ab} \)

This matches option **d**.

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Would you like more details or clarifications on this solution?

Here are 5 related questions for further practice:
1. How do you simplify expressions involving fractional exponents?
2. What happens when you multiply powers of the same base?
3. How does taking the inverse affect the exponents in a fraction?
4. What are the rules for dividing expressions with exponents?
5. How would the result change if the exponents were negative?

**Tip**: Always break down complex expressions step by step, focusing on simplifying one part at a time!

Hasil dari (a^(2/3) / b^(1/2))^-1 × (a^(2/3) * b^(1/2))^2 * a^(1/3) / b^(1/2) adalah ...

Explore how to simplify expressions with fractional exponents. This problem involves applying the laws of exponents and handling inverse operations, suitable for students in Grades 10-12.

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