Question

What index should the root form of the expression 12 ^ (5/8) * 12 ^ (- 1/2) have?

Answer 1

Are you sure

Answer 2

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).

Answer 3

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).