x to the power -7/2 into 2x to the power -1/2=?

2x^-4?

(2x)^(-1/2) / x^(-7/2)

x^(7/2) / 2^(1/2)*x^(1/2)

x^3/√2

To find the product of these two expressions, you need to multiply the numerical coefficients (if any) and then add the exponents. Let's break it down step by step:

1. Start by multiplying the numerical coefficients, which in this case is 2. So the result becomes:

2 * (x^(-7/2)) * (2x^(-1/2))

2. Since we are dealing with exponents, we can apply the exponent rule which states that when you multiply two variables with the same base, you keep the base and add the exponents. Therefore, for the x term, we add the exponents (-7/2 + -1/2) giving us -8/2.

The expression simplifies to:

2 * (x^(-8/2))

3. Continuing the simplification, -8/2 can be further simplified to -4.

The expression becomes:

2 * (x^(-4))

So, the final answer is 2x^(-4).