Algebraic Exponents Simplification

CMAT 2025 · Quantitative Techniques & Data Interpretation · Medium · Algebra

The value of $\left(\frac{x^b}{x^a}\right)^{a^2+ab+b^2} \left(\frac{x^c}{x^b}\right)^{b^2+bc+c^2} \left(\frac{x^a}{x^c}\right)^{c^2+ca+a^2}$ is:

Answer

Each term simplifies using $(x^{a-b})^{a^2+ab+b^2} = x^{a^3-b^3}$ . Multiplying all three terms gives $x^{(a^3-b^3)+(b^3-c^3)+(c^3-a^3)} = x^0 = 1$ .

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