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If a^3 * a^(-2) = a^x, what is the value of x? (2023)

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Question: If a^3 * a^(-2) = a^x, what is the value of x? (2023)

Options:

  1. 1
  2. 0
  3. -1
  4. 3

Correct Answer: 1

Exam Year: 2023

Solution: 

Using the property of exponents, a^3 * a^(-2) = a^(3 - 2) = a^1, hence x = 1.

If a^3 * a^(-2) = a^x, what is the value of x? (2023)

Practice Questions

Q1
If a^3 * a^(-2) = a^x, what is the value of x? (2023)
  1. 1
  2. 0
  3. -1
  4. 3

Questions & Step-by-Step Solutions

If a^3 * a^(-2) = a^x, what is the value of x? (2023)
  • Step 1: Start with the equation a^3 * a^(-2) = a^x.
  • Step 2: Use the property of exponents that states a^m * a^n = a^(m + n).
  • Step 3: Apply this property to combine the exponents: a^3 * a^(-2) becomes a^(3 + (-2)).
  • Step 4: Simplify the exponent: 3 + (-2) = 3 - 2 = 1.
  • Step 5: Now we have a^(3 - 2) = a^1.
  • Step 6: Since a^1 = a^x, we can conclude that x = 1.
  • Properties of Exponents – Understanding how to manipulate exponents, specifically the rule that states a^m * a^n = a^(m+n).
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