Let's solve the equation \( (2x)^2 = 64 \):

### Step 1: Simplify the equation
We have \( (2x)^2 = 64 \), which means we square \( 2x \):
\[
(2x)^2 = 4x^2
\]
So the equation becomes:
\[
4x^2 = 64
\]

### Step 2: Solve for \( x^2 \)
Now, divide both sides by 4 to isolate \( x^2 \):
\[
x^2 = \frac{64}{4} = 16
\]

### Step 3: Solve for \( x \)
To solve for \( x \), take the square root of both sides:
\[
x = \pm \sqrt{16} = \pm 4
\]

### Final Answer:
The solutions are \( x = 4 \) or \( x = -4 \).

Would you like further details or have any questions? 

Here are 5 related questions:
1. How do you solve \( (3x)^2 = 81 \)?
2. What happens when you square a negative number?
3. How do you graph \( y = 4x^2 \)?
4. What is the difference between squaring and taking the square root of a number?
5. How do you factor quadratic equations like \( x^2 - 16 = 0 \)?

**Tip:** When squaring terms with variables, always apply the exponent to both the coefficient and the variable.

Learn how to solve the quadratic equation (2x)^2 = 64 step-by-step. This problem focuses on simplifying exponents and using the square root method to find solutions. Ideal for students in Grades 8-10.

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