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]
