Question

1. \\( \frac{4x^{-4}y^{0}}{-x^{-2}} \\)

Explanation:

Step1: Simplify \( y^0 \)

Any non - zero number to the power of 0 is 1, so \( y^0 = 1 \). The expression becomes \( \frac{4x^{-4}\times1}{-x^{-2}}=\frac{4x^{-4}}{-x^{-2}} \)

Step2: Use the rule of exponents \( \frac{a^m}{a^n}=a^{m - n} \)

For the \( x \) terms, \( \frac{x^{-4}}{x^{-2}}=x^{-4-(-2)}=x^{-4 + 2}=x^{-2} \)
And the coefficient is \( \frac{4}{-1}=-4 \)
So the expression simplifies to \( - 4x^{-2} \), or we can write it as \( \frac{-4}{x^{2}} \) (using the rule \( a^{-n}=\frac{1}{a^{n}} \))

Answer:

\( - \frac{4}{x^{2}} \) (or \( - 4x^{-2} \))