Question
What index should the root form of the expression 12 ^ (5/8) * 12 ^ (- 1/2) have?
Answers
GPT 3.5
To simplify the expression 12^(5/8) * 12^(-1/2), we need to combine the two exponents. The general rule for multiplying exponents with the same base is to add the exponents together.
So the new exponent would be (5/8) + (-1/2). To add the fractions, we need to find a common denominator. Since 8 and 2 have a common multiple of 8, we can write -1/2 as -4/8.
Now the new exponent would be (5/8) + (-4/8) = 1/8.
Therefore, the root form of the expression 12^(5/8) * 12^(-1/2) would be 12^(1/8).
So the new exponent would be (5/8) + (-1/2). To add the fractions, we need to find a common denominator. Since 8 and 2 have a common multiple of 8, we can write -1/2 as -4/8.
Now the new exponent would be (5/8) + (-4/8) = 1/8.
Therefore, the root form of the expression 12^(5/8) * 12^(-1/2) would be 12^(1/8).
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Are you sure
GPT 3.5
Apologies for the incorrect response. You are right. Let's re-evaluate the expression:
To simplify the expression 12^(5/8) * 12^(-1/2), we add the exponents.
The expression becomes 12^((5/8) + (-1/2)) = 12^(5/8 - 4/8) = 12^(1/8).
Therefore, the root form of the expression 12^(5/8) * 12^(-1/2) is indeed 12^(1/8).
To simplify the expression 12^(5/8) * 12^(-1/2), we add the exponents.
The expression becomes 12^((5/8) + (-1/2)) = 12^(5/8 - 4/8) = 12^(1/8).
Therefore, the root form of the expression 12^(5/8) * 12^(-1/2) is indeed 12^(1/8).