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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)
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0
-1
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Questions & Step-by-Step Solutions
If a^3 * a^(-2) = a^x, what is the value of x? (2023)
Steps
Concepts
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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