7

Set 8: Exponential Functions

Explanation

Answer: A

Express 1e3x\frac{1}{e^{3x}} with positive exponents.

A.

e3xe^{-3x}

✓ Correct
B.

e3x-e^{3x}

C.

e3/xe^{3/x}

D.

3xe\frac{3x}{e}

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Use negative exponent rule. 1. Rule: 1am=am\frac{1}{a^m} = a^{-m}. 2. Apply: 1e3x=e3x\frac{1}{e^{3 x}} = e^{-3 x}. Strategic Tip: Negative exponents indicate reciprocals. Choice B is incorrect because negative sign goes in exponent, not coefficient. Choice C is incorrect because this changes the expression entirely. Choice D is incorrect because this is not equivalent.

Key Steps:

The correct answer is e3xe^{-3x}

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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