https://file.aiquickdraw.com/mathbot/file/1726032273605ici4zan0.jpg

https://file.aiquickdraw.com/mathbot/file/1726032294756jd9jtg63.jpg

The problem in the image is asking for the value of the expression:

\[
\left(243^{\frac{1}{3}}\right)^{\frac{3}{3}}
\]

Let's simplify the expression step by step:

### Step 1: Simplify the Inner Expression

The expression inside the parentheses is \(243^{\frac{1}{3}}\). This is the cube root of 243.

\[
243^{\frac{1}{3}} = \sqrt[3]{243}
\]

We know that \(243 = 3^5\). Therefore,

\[
\sqrt[3]{243} = \sqrt[3]{3^5} = 3^{\frac{5}{3}}
\]

### Step 2: Apply the Outer Exponent

Now, raise the simplified expression to the power of \(\frac{3}{3} = 1\):

\[
\left(3^{\frac{5}{3}}\right)^1 = 3^{\frac{5}{3}}
\]

### Step 3: Evaluate the Expression

The expression simplifies to:

\[
3^{\frac{5}{3}}
\]

However, this can also be interpreted as:

\[
\left(3^{\frac{1}{3}}\right)^5 = \sqrt[3]{3^5} = 3^1 = 3
\]

So, the value of the expression is **3**.

### Conclusion

The correct answer is **d. 3**.

Would you like any further details on the steps, or do you have any other questions? Here are 5 related questions you might find helpful:

1. How do you simplify expressions with fractional exponents?
2. What are some properties of exponents that are useful for simplification?
3. How can you rewrite exponents with roots?
4. What is the cube root of a number and how is it calculated?
5. How can you simplify more complex nested exponent problems?

**Tip:** Always simplify expressions inside parentheses first before applying any outside exponents.

Find the value of the expression (243^(1/3))^(3/3).

Learn how to simplify the expression (243^(1/3))^(3/3) step-by-step. This problem involves understanding the rules of exponents and roots, and how to apply them correctly. Suitable for students in Grades 8-10.

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