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Nes Simplifi ((x^(a))/(x^(b)))^(b+k-a)((x^(c))/(x^(a)))^(c+a-b)((x^(a))/(x^(b)))^(a+b-c)

Nes Simplifi (xaxb)b+k−a(xcxa)c+a−b(xaxb)a+b−c \left(\frac{x^{a}}{x^{b}}\right)^{b+k-a}\left(\frac{x^{c}}{x^{a}}\right)^{c+a-b}\left(\frac{x^{a}}{x^{b}}\right)^{a+b-c}

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Q. Nes Simplifi (xaxb)b+k−a(xcxa)c+a−b(xaxb)a+b−c \left(\frac{x^{a}}{x^{b}}\right)^{b+k-a}\left(\frac{x^{c}}{x^{a}}\right)^{c+a-b}\left(\frac{x^{a}}{x^{b}}\right)^{a+b-c}
  1. Simplify Fractions: Step 11: Simplify each fraction using the properties of exponents.\newline(xa)/(xb)=xa−b(x^a)/(x^b) = x^{a-b},\newline(xc)/(xa)=xc−a(x^c)/(x^a) = x^{c-a},\newline(xa)/(xb)=xa−b(x^a)/(x^b) = x^{a-b}.
  2. Apply Exponents: Step 22: Apply the exponents to each simplified fraction.\newline(xa−b)b+k−a=x(a−b)(b+k−a)(x^{a-b})^{b+k-a} = x^{(a-b)(b+k-a)},\newline(xc−a)c+a−b=x(c−a)(c+a−b)(x^{c-a})^{c+a-b} = x^{(c-a)(c+a-b)},\newline(xa−b)a+b−c=x(a−b)(a+b−c)(x^{a-b})^{a+b-c} = x^{(a-b)(a+b-c)}.
  3. Multiply Results: Step 33: Multiply the results using the property xm⋅xn=xm+nx^m \cdot x^n = x^{m+n}.\newlinex(a−b)(b+k−a)+(c−a)(c+a−b)+(a−b)(a+b−c)x^{(a-b)(b+k-a) + (c-a)(c+a-b) + (a-b)(a+b-c)}.
  4. Expand and Simplify: Step 44: Expand and simplify the exponent.\newline(a−b)(b+k−a)=ab−a2+bk−ba(a-b)(b+k-a) = ab - a^2 + bk - ba,\newline(c−a)(c+a−b)=c2−ca+ac−ab(c-a)(c+a-b) = c^2 - ca + ac - ab,\newline(a−b)(a+b−c)=a2−ab+ab−b2(a-b)(a+b-c) = a^2 - ab + ab - b^2.\newlineAdding these,\newlineab−a2+bk−ba+c2−ca+ac−ab+a2−ab+ab−b2ab - a^2 + bk - ba + c^2 - ca + ac - ab + a^2 - ab + ab - b^2,\newlineSimplifies to,\newlinebk+c2−ca+ac−b2bk + c^2 - ca + ac - b^2.

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