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We are asked to solve the exponential equation \( 4^r = 64 \).

### Step-by-step solution:

1. Express 64 as a power of 4:
   - We know that \( 64 = 4^3 \), because \( 4 \times 4 \times 4 = 64 \).

2. Rewrite the equation:
   \[
   4^r = 4^3
   \]

3. Since the bases are the same, we can equate the exponents:
   \[
   r = 3
   \]

Thus, the solution is:
\[
r = 3
\]

Would you like more details on the steps?

Here are 5 related questions:
1. How would you solve \( 2^r = 32 \)?
2. What happens if the base isn't the same in both sides of the equation?
3. How would you solve \( 4^r = 100 \) without a clear power relationship?
4. What are logarithms, and how do they help in solving exponential equations?
5. How do exponent rules apply to equations like \( (4^r)^2 = 64 \)?

**Tip:** Always try to express numbers as powers of the same base when solving exponential equations.

Learn how to solve the exponential equation 4^r = 64 with a clear step-by-step solution. This problem teaches key concepts of algebra and exponents, suitable for students in Grades 6-8.

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