https://file.aiquickdraw.com/mathbot/file/17270167776388hm426l0.jpg

The expression given in the image is:

\[
(64x^4)^{0.5} \times 4x^{-2}
\]

Let's solve it step by step.

### Step 1: Simplify \((64x^4)^{0.5}\)
We can apply the exponent rule \((a^m \cdot b^m) = (ab)^m\):

\[
(64x^4)^{0.5} = 64^{0.5} \cdot (x^4)^{0.5}
\]

Now, simplifying both parts:
\[
64^{0.5} = \sqrt{64} = 8
\]
\[
(x^4)^{0.5} = x^{4 \cdot 0.5} = x^2
\]

Thus, we get:
\[
(64x^4)^{0.5} = 8x^2
\]

### Step 2: Multiply by \(4x^{-2}\)
Now, multiply the result by \(4x^{-2}\):

\[
8x^2 \times 4x^{-2} = (8 \times 4) \cdot (x^2 \cdot x^{-2}) = 32 \cdot x^{2 + (-2)} = 32 \cdot x^0
\]

Since \(x^0 = 1\), this simplifies to:
\[
32 \cdot 1 = 32
\]

### Final Answer:
The value of the expression is \(32\).

Would you like more details or have any questions? Here are 5 related questions you might consider:

1. What are the general rules for simplifying expressions with exponents?
2. How does the exponent rule \((ab)^m = a^m \cdot b^m\) work in other cases?
3. What is the significance of \(x^0 = 1\) for all non-zero \(x\)?
4. How do fractional exponents relate to roots (e.g., \(a^{0.5} = \sqrt{a}\))?
5. Can you explain how negative exponents affect multiplication of terms?

**Tip:** Remember that multiplying powers of the same base adds their exponents!

Find the value of (64x^4)^0.5 × 4x^−2.

Learn how to simplify the expression (64x^4)^0.5 × 4x^−2 using exponent rules. This problem explores key algebraic concepts like simplification of radicals and multiplication of powers. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation