What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(4x)?

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Question: What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(4x)?

Options:

Correct Answer: 2^(x)

Solution:

Using the properties of exponents, we combine the exponents: (3x + 2x - 4x) = x, thus the result is 2^x.

What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(4x)?

What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(4x)?

Step 1: Identify the expression to simplify: 2^(3x) * 2^(2x) / 2^(4x).
Step 2: Use the property of exponents that states a^m * a^n = a^(m+n) to combine the first two terms: 2^(3x) * 2^(2x) becomes 2^(3x + 2x).
Step 3: Calculate the sum of the exponents: 3x + 2x = 5x, so now we have 2^(5x) / 2^(4x).
Step 4: Use the property of exponents that states a^m / a^n = a^(m-n) to simplify: 2^(5x) / 2^(4x) becomes 2^(5x - 4x).
Step 5: Calculate the difference of the exponents: 5x - 4x = x, so we have 2^x.
Step 6: The final simplified result is 2^x.

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