https://file.aiquickdraw.com/mathbot/file/1724161012796u7vw2bvy.jpg

The expression in the image is \(\sqrt[3]{\sqrt{a^2}}\).

Let's simplify it using the laws of exponents.

### Step 1: Rewrite the radicals as exponents.
- The square root \(\sqrt{a^2}\) is equivalent to \(a^{2/2}\) which simplifies to \(a^1\).
- The cube root \(\sqrt[3]{a}\) is equivalent to raising \(a\) to the power \(1/3\).

So, \(\sqrt[3]{\sqrt{a^2}}\) can be rewritten as:
\[
\left(a^1\right)^{1/3}
\]

### Step 2: Apply the power of a power rule.
- The rule \((a^m)^n = a^{m \cdot n}\) allows us to multiply the exponents.

Thus, \(\left(a^1\right)^{1/3}\) simplifies to:
\[
a^{1/3}
\]

### Final Answer:
\[
\sqrt[3]{\sqrt{a^2}} = a^{1/3}
\]

This is the simplified form of the expression using the laws of exponents.

Would you like more details or have any questions?

### Related Questions:
1. What would be the result if the exponent was \(\sqrt[4]{\sqrt{a^8}}\)?
2. Can you apply the same method to simplify \(\sqrt[5]{\sqrt[3]{a^6}}\)?
3. How does the simplification change if the base is not a variable but a constant?
4. What if the original expression involved a negative exponent?
5. How would you approach a similar expression with multiple variables, like \(\sqrt[3]{\sqrt{a^2b^3}}\)?

### Tip:
When simplifying expressions involving roots and exponents, always convert roots to fractional exponents first. This makes it easier to apply exponent rules consistently.

Learn how to simplify the expression \(\sqrt[3]{\sqrt{a^2}}\) step-by-step using exponent rules and simplification of radicals. Understand the power of a power rule and its application in algebraic expressions. Suitable for high school students and anyone interested in advanced algebra concepts.

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