Simplify $\left(\frac{x^m}{x^n}\right)^{

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

Simplify $\left(\frac{x^m}{x^n}\right)^{m+n}.\left(\frac{x^n}{x^p}\right)^{n+p}.(x^p×x^m)^{p-m}$

Options:

$mnp$

$m^2-p^2+n^2$

Correct Answer:

Explanation:

( x^m-n )^m+n × ( x^n-p )^n+p × ( x^p+m )^p-m

⇒ (x)^{m² - n²} × (x)^{n² -p²} × (x)^{p² - m²}

⇒ (x)^{(m² - n² + n² - p² + p² - m²)}

Here, (m² - n² + n² - p² + p² - m² = 0 )

Therefore,

⇒ x⁰= 1