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The given expression is \( 32^{\frac{3}{5}} \times 36^{-\frac{1}{2}} \). We are asked to compute this and express the result as an integer or a fraction in its simplest form.

Let's break this down step by step:

1. First, evaluate \( 32^{\frac{3}{5}} \):
   - \( 32 \) can be expressed as \( 2^5 \).
   - So, \( 32^{\frac{3}{5}} = (2^5)^{\frac{3}{5}} = 2^3 = 8 \).

2. Next, evaluate \( 36^{-\frac{1}{2}} \):
   - \( 36 \) can be expressed as \( 6^2 \).
   - So, \( 36^{-\frac{1}{2}} = (6^2)^{-\frac{1}{2}} = 6^{-1} = \frac{1}{6} \).

3. Now, multiply the results:
   \[
   32^{\frac{3}{5}} \times 36^{-\frac{1}{2}} = 8 \times \frac{1}{6} = \frac{8}{6} = \frac{4}{3}.
   \]

Thus, the final answer is \( \frac{4}{3} \).

Would you like further details or have any questions? Here are 5 related questions to expand on this:

1. How do you simplify fractional exponents involving roots?
2. How do negative exponents affect the result of an expression?
3. What is the general rule for multiplying powers with different bases?
4. Can you apply fractional exponents to any number, or are there restrictions?
5. How would the result change if the exponents were different in this example?

**Tip:** When working with fractional exponents, try expressing the base as a power of a simpler number to make calculations easier.

Work out 32^(3/5) × 36^(-1/2). Give your answer as an integer or as a fraction in its simplest form.

Learn how to simplify the exponential expression 32^(3/5) × 36^(-1/2) with a step-by-step guide. This problem covers key concepts such as fractional and negative exponents, suitable for students in Grades 10-12.

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