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Example

Evaluating x2x^2 versus 3x3^x at x=4x = 4

When a variable appears in an exponential expression, it is important to identify whether the variable is the base or the exponent, because the evaluation process differs:

Evaluating x2x^2 at x=4x = 4: The variable is the base. Replace xx with 44 to get 424^2. Expand using the definition of exponents: 44=164 \cdot 4 = 16.

Evaluating 3x3^x at x=4x = 4: The variable is the exponent. Replace xx with 44 to get 343^4. Expand: 3333=813 \cdot 3 \cdot 3 \cdot 3 = 81.

Although both expressions involve the same number 44, the results (1616 versus 8181) differ because the variable plays a different role in each expression.

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Updated 2026-04-21

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