https://file.aiquickdraw.com/mathbot/file/1726591744260qb11yob1.jpg

Let's solve the given expressions step by step:

### Problem (a):
\[
(-243)^{\frac{1}{5}}
\]

This is asking for the fifth root of \(-243\). 

- Since \(-243\) is negative, we need to check if there exists a real number that when raised to the fifth power results in \(-243\). 
- The fifth root of \(-243\) is \(-3\) because:
  \[
  (-3)^5 = -243
  \]

So, the solution for (a) is:
\[
\boxed{-3}
\]

### Problem (b):
\[
(-49)^{\frac{1}{2}}
\]

This is asking for the square root of \(-49\).

- The square root of a negative number does not exist in the set of real numbers (it belongs to the set of complex numbers). Therefore, this expression is **not a real number**.

So, the answer for (b) is:
\[
\boxed{\text{Not a real number}}
\]

Let me know if you would like further clarification or more details! Here are five related questions to consider:

1. What is the cube root of \(-8\)?
2. Can you find the fourth root of 16?
3. What is the principal square root of 25?
4. How do you calculate the cube root of a negative number?
5. Why are even roots of negative numbers not real?

**Tip**: When dealing with roots of negative numbers, odd roots can result in real numbers, while even roots lead to complex numbers!

Evaluate the following: (a) (-243)^(1/5), (b) (-49)^(1/2). Click on 'Not a real number' if applicable.

Explore how to evaluate roots of negative numbers, including finding the fifth root of -243 and understanding why the square root of -49 is not a real number. A step-by-step guide for students in Grades 8-10.

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