What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(5x)?

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Question: What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(5x)?

Options:

Correct Answer: 2^(3x + 2x - 5x)

Solution:

Using the properties of exponents, we combine the exponents: 2^(3x + 2x - 5x) = 2^0 = 1.

What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(5x)?

What is the result of simplifying the expression 2^(3x) * 2^(2x) / 2^(5x)?

Step 1: Identify the expression to simplify: 2^(3x) * 2^(2x) / 2^(5x).
Step 2: Use the property of exponents that says a^m * a^n = a^(m+n) to combine the first two terms: 2^(3x + 2x).
Step 3: Calculate the sum of the exponents: 3x + 2x = 5x. So, we have 2^(5x) in the numerator.
Step 4: Now, rewrite the expression: (2^(5x)) / (2^(5x)).
Step 5: Use the property of exponents that says a^m / a^n = a^(m-n) to simplify: 2^(5x - 5x).
Step 6: Calculate the exponent: 5x - 5x = 0. So, we have 2^0.
Step 7: Recall that any number raised to the power of 0 is 1. Therefore, 2^0 = 1.

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