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If a^m * a^n = a^p, what is the value of p?

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Question: If a^m * a^n = a^p, what is the value of p?

Options:

  1. m + n
  2. m - n
  3. m * n
  4. m / n

Correct Answer: m + n

Solution: 

According to the laws of exponents, when multiplying like bases, we add the exponents: p = m + n.

If a^m * a^n = a^p, what is the value of p?

Practice Questions

Q1
If a^m * a^n = a^p, what is the value of p?
  1. m + n
  2. m - n
  3. m * n
  4. m / n

Questions & Step-by-Step Solutions

If a^m * a^n = a^p, what is the value of p?
  • Step 1: Identify the expression a^m * a^n. Here, 'a' is the base and 'm' and 'n' are the exponents.
  • Step 2: Recall the rule of exponents that states when you multiply two expressions with the same base, you add the exponents.
  • Step 3: Apply the rule: a^m * a^n = a^(m + n).
  • Step 4: This means that p, which is the exponent in a^p, is equal to m + n.
  • Step 5: Therefore, the value of p is m + n.
  • Laws of Exponents – When multiplying powers with the same base, the exponents are added together.
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