Sure, let’s simplify the given expression step-by-step.
Given:
[tex]\[
(14 x^3 y^{-4})(4 x^{-5} y^4)
\][/tex]
1. Combine the coefficients:
[tex]\[
14 \cdot 4 = 56
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms using the properties of exponents:
[tex]\[
x^3 \cdot x^{-5} = x^{3 + (-5)} = x^{-2}
\][/tex]
3. Combine the [tex]\(y\)[/tex] terms using the properties of exponents:
[tex]\[
y^{-4} \cdot y^4 = y^{-4 + 4} = y^0
\][/tex]
Recall that any number raised to the power of 0 is 1:
[tex]\[
y^0 = 1
\][/tex]
Putting everything together, we get:
[tex]\[
56 \cdot x^{-2} \cdot 1 = 56 x^{-2}
\][/tex]
Recall that [tex]\( x^{-2} \)[/tex] can be written as [tex]\( \frac{1}{x^2} \)[/tex]:
[tex]\[
56 x^{-2} = 56 \cdot \frac{1}{x^2} = \frac{56}{x^2}
\][/tex]
Therefore, the equivalent expression is:
[tex]\[
\boxed{\frac{56}{x^2}}
\][/tex]
The correct answer is:
A. [tex]\(\frac{56}{x^2}\)[/tex]
