Select the correct answer.

Which expression is equivalent to the given expression?

[tex]\[
\left(14 x^3 y^{-4}\right)\left(4 x^{-5} y^4\right)
\][/tex]

A. [tex]\(\frac{56}{x^2}\)[/tex]

B. [tex]\(56 x^2 y\)[/tex]

C. [tex]\(\frac{56 y}{x^2}\)[/tex]

D. [tex]\(56 x^2\)[/tex]



Answer :

To determine which expression is equivalent to [tex]\(\left(14 x^3 y^{-4}\right)\left(4 x^{-5} y^4\right)\)[/tex], we need to simplify the product step by step.

1. Simplify the coefficients:
[tex]\[ 14 \cdot 4 = 56 \][/tex]

2. Combine the powers of [tex]\(x\)[/tex]:
[tex]\[ x^3 \cdot x^{-5} = x^{3 + (-5)} = x^{-2} \][/tex]

3. Combine the powers of [tex]\(y\)[/tex]:
[tex]\[ y^{-4} \cdot y^4 = y^{-4 + 4} = y^0 \][/tex]
Since [tex]\(y^0 = 1\)[/tex], it can be ignored in the multiplication.

Putting it all together, the simplified expression is:
[tex]\[ 56 x^{-2} \][/tex]

To express [tex]\(56 x^{-2}\)[/tex] in a more conventional format, [tex]\(x^{-2} = \frac{1}{x^2}\)[/tex]. So:
[tex]\[ 56 x^{-2} = \frac{56}{x^2} \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{\frac{56}{x^2}} \][/tex]

So, the correct answer is:
A. [tex]\(\frac{56}{x^2}\)[/tex]