https://file.aiquickdraw.com/mathbot/file/17265495764601wxxyiwo.jpg

It seems that the OCR did not capture the text properly. From visual inspection, the expression to simplify appears to be:

\[
64^{\frac{3}{2}} \cdot 4^{\frac{7}{2}}
\]

Let's proceed to simplify this expression.

First, rewrite the terms with common bases:
- \( 64 = 4^3 \), so \( 64^{\frac{3}{2}} = (4^3)^{\frac{3}{2}} = 4^{\frac{9}{2}} \).

Now, the expression becomes:

\[
4^{\frac{9}{2}} \cdot 4^{\frac{7}{2}} = 4^{\frac{9}{2} + \frac{7}{2}} = 4^{\frac{16}{2}} = 4^8
\]

Finally:

\[
4^8 = 65536
\]

So, the simplified result is:

\[
65536
\]

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. How do you simplify expressions with fractional exponents?
2. What are the rules for multiplying exponents with the same base?
3. How can you express any number as a power of a smaller base?
4. What is the significance of fractional powers (like \(x^{\frac{1}{2}}\))?
5. How do you approach simplifying complex exponent expressions?

**Tip:** Always look for a common base when simplifying expressions with exponents. It simplifies the process significantly!

Simplify the expression 64^(3/2) * 4^(7/2).

Learn how to simplify the expression 64^(3/2) * 4^(7/2) using the laws of exponents. This step-by-step guide helps students understand key exponent rules. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation