Algebra-2

Question Analysis
question involves an exponential equation with related bases (27 and 9, both powers of 3). The main focus is on rewriting both bases as powers of 3, applying the Power of a Power Rule to simplify exponents, and solving the resulting linear equation for x.

Key Concept Explanation
The Power of a Power Rule states (where , ). By rewriting 27 as and 9 as , we can use this rule to make both sides of the equation have the same base (3), allowing us to equate exponents.

Step-by-step Solution
1. Rewrite 27 and 9 as powers of 3: and . Substitute into the equation: .
2. Apply the Power of a Power Rule: Multiply exponents on both sides: , which simplifies to

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