Which expression is equivalent to the following for all values where each variable is defined?

Question

Which expression is equivalent to the following for all values where each variable is defined?

(2x^5y)(4xy^-2)

A. 8x^6y

B. (8x^6)/y

C. (6x^5)/y^2

D. 6x^6y

Answer 1

The expression (2x^5y)(4xy^-2) can be simplified by multiplying the coefficients and adding the exponents of the variables:

(2x^5y)(4xy^-2) = 2 * 4 * (x^5 * x^1) * (y^1 * y^-2) = 8x^6y^(-1+2) = 8x^6y^1

Therefore, the expression is equivalent to 8x^6y.

The correct answer is A. 8x^6y.

Answer 2

Apologies for the incorrect response. Let's go through the simplification again:

(2x^5y)(4xy^-2) = 2 * 4 * x^5 * x * y * y^-2
= 8x^(5+1) * y^(1-2)
= 8x^6 * y^(-1)
= 8x^6/y

Therefore, the expression is equivalent to (8x^6)/y.

The correct answer is B. (8x^6)/y.

Answer 3

I apologize for the earlier incorrect response. Thank you for pointing out the mistake. I'm glad we have corrected it. Please don't hesitate to reach out if you have any further questions.

Which expression is equivalent to the following for all values where each variable is defined?

The expression (2x^5y)(4xy^-2) can be simplified by multiplying the coefficients and adding the exponents of the variables:

Wrong

Apologies for the incorrect response. Let's go through the simplification again:

Right

I apologize for the earlier incorrect response. Thank you for pointing out the mistake. I'm glad we have corrected it. Please don't hesitate to reach out if you have any further questions.