https://file.aiquickdraw.com/mathbot/file/1727361069448ilipvszx.jpg

The problem is asking to evaluate:

\[
4^{\frac{5}{2}} \times 4^{\frac{1}{2}}
\]

### Solution:

Using the property of exponents:

\[
a^m \times a^n = a^{m+n}
\]

We can apply this rule since both terms have the same base \(4\):

\[
4^{\frac{5}{2}} \times 4^{\frac{1}{2}} = 4^{\frac{5}{2} + \frac{1}{2}} = 4^{\frac{6}{2}} = 4^3
\]

Now, calculate \(4^3\):

\[
4^3 = 64
\]

Thus, the correct answer is:

\[
\boxed{64}
\]

Would you like more details or have any other questions?

### Related Questions:
1. How do you simplify expressions with exponents and the same base?
2. How does the exponent addition rule work for different bases?
3. What is the value of \(4^2\)?
4. How would this problem change if the base was \(5\) instead of \(4\)?
5. What is the general rule for multiplying fractional exponents?

**Tip:** When working with exponents, remember that adding exponents is only valid when the base is the same.

Learn how to simplify the expression 4^(5/2) × 4^(1/2) using exponent addition rules. This problem covers key concepts of exponents and multiplication of powers with the same base. Suitable for students in Grades 8-10.

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