If a^m * a^n = a^p, which of the following is true?

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Question: If a^m * a^n = a^p, which of the following is true?

Options:

Correct Answer: m + n = p

Solution:

The property of exponents states that when multiplying like bases, you add the exponents: m + n = p.

If a^m * a^n = a^p, which of the following is true?

If a^m * a^n = a^p, which of the following is true?

Step 1: Identify the bases in the expression a^m * a^n. Here, the base is 'a'.
Step 2: Look at the exponents in the expression. They are 'm' and 'n'.
Step 3: Recall the property of exponents that states when you multiply two numbers with the same base, you add their exponents.
Step 4: Apply this property to the expression: a^m * a^n = a^(m + n).
Step 5: Set the result equal to a^p, which gives us a^(m + n) = a^p.
Step 6: Since the bases are the same, we can conclude that the exponents must be equal: m + n = p.

Properties of Exponents – When multiplying numbers with the same base, the exponents are added together.