https://file.aiquickdraw.com/mathbot/file/1729810109070ompycedj.jpg

Let's simplify the expressions in the image step by step.

### First Expression:
\[
\frac{3}{32} \div \frac{5}{5}
\]
Dividing by a fraction is the same as multiplying by its reciprocal. So, we rewrite the division as:
\[
\frac{3}{32} \times \frac{5}{5}
\]
Since \(\frac{5}{5} = 1\), the expression simplifies to:
\[
\frac{3}{32}
\]

### Second Expression:
\[
\left(\frac{1}{9}\right)^{\frac{3}{2}}
\]
This is the fractional exponent \(\frac{3}{2}\), which represents a square root followed by cubing. First, find the square root of \(\frac{1}{9}\):
\[
\sqrt{\frac{1}{9}} = \frac{1}{3}
\]
Now, cube the result:
\[
\left(\frac{1}{3}\right)^3 = \frac{1}{27}
\]

### Final Answers:
1. \(\frac{3}{32}\)
2. \(\frac{1}{27}\)

Would you like further details or have any questions?

Here are some related questions:
1. How do you handle division of fractions generally?
2. What is the general approach for simplifying fractional exponents?
3. Can fractional exponents be negative? What would that mean?
4. How do you convert fractional exponents to radical form?
5. How does multiplying fractions affect their values?

**Tip:** When simplifying fractions with exponents, always start by breaking down the operations, such as roots and powers.

Simplify. Write your answers without exponents.

Learn how to simplify complex fractions and fractional exponents step by step. This example covers dividing fractions by converting to multiplication by the reciprocal and simplifying exponents using radical form. Suitable for students in Grades 8-10.

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