Algebra-2

Question Analysis
This question involves an exponential equation with related bases (16 and 64, both powers of 2). The main focus is on rewriting both bases as powers of 2, applying the Power of a Power Rule to simplify exponents, and then solving the resulting linear equation for x.

Key Concept Explanation
The Power of a Power Rule states (where , ). By rewriting 16 as and 64 as , we can use this rule to make both sides of the equation have the same base (2), allowing us to equate exponents.

Step-by-step Solution
1. Rewrite 16 and 64 as powers of 2: and . Substitute into the equation: .
2. Apply the Power of a Power Rule: Multiply exponents on both sides: