https://file.aiquickdraw.com/mathbot/file/1727173909492l23ci6zj.jpg

The expression given in the image is \((2x)^3 \times (2x)^2\).

We can simplify this expression step by step:

### Step 1: Apply the power rule
When raising a product to a power, each term inside the parentheses is raised to that power:

\[
(2x)^3 = 2^3 \cdot x^3 = 8x^3
\]
\[
(2x)^2 = 2^2 \cdot x^2 = 4x^2
\]

### Step 2: Multiply the simplified expressions
Now multiply the two simplified expressions:
\[
8x^3 \times 4x^2 = (8 \times 4) \cdot (x^3 \times x^2)
\]

\[
= 32 \cdot x^{3+2} = 32x^5
\]

So, the expression \((2x)^3 \times (2x)^2\) is equivalent to \(32x^5\).

Would you like more details or have any other questions?

### Related questions:
1. How do you simplify expressions with exponents?
2. What is the power of a product rule in algebra?
3. Can you explain the laws of exponents with examples?
4. How does multiplying terms with the same base affect their exponents?
5. How do you factor polynomial expressions with powers?

**Tip**: Remember, when multiplying terms with the same base, add their exponents!

Which expression is equivalent to (2x)^3 × (2x)^2?

Learn how to simplify the expression (2x)^3 × (2x)^2 using the laws of exponents. This problem involves applying the power of a product rule and multiplying terms with the same base, resulting in 32x^5. Ideal for students in Grades 8-10.

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