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((y^(-2))^(-6))/(-x^(4)y^(-4)*-xy^(4))

(y−2)−6−x4y−4⋅−xy4 \frac{\left(y^{-2}\right)^{-6}}{-x^{4} y^{-4} \cdot-x y^{4}}

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Full solution

Q. (y−2)−6−x4y−4⋅−xy4 \frac{\left(y^{-2}\right)^{-6}}{-x^{4} y^{-4} \cdot-x y^{4}}
  1. Simplify numerator: First, simplify the numerator (y−2)−6(y^{-2})^{-6}.\newlineUsing the power of a power rule, (am)n=am∗n(a^m)^n = a^{m*n},\newline(y−2)−6=y(−2)∗(−6)=y12(y^{-2})^{-6} = y^{(-2)*(-6)} = y^{12}.
  2. Simplify denominator: Next, simplify the denominator −x4y−4⋅−xy4-x^{4}y^{-4}\cdot -xy^{4}. First, simplify −x4⋅−x=x4+1=x5-x^{4} \cdot -x = x^{4+1} = x^{5}. Then, simplify y−4⋅y4=y−4+4=y0=1y^{-4} \cdot y^{4} = y^{-4+4} = y^{0} = 1. So, the denominator becomes x5x^{5}.
  3. Divide numerator by denominator: Now, divide the simplified numerator by the simplified denominator. y12/x5y^{12} / x^5.

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