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Exercise

$\frac{\left(-1\right)^n\left(x-2\right)^n}{3^n\sqrt{n^2+1}}$

Step-by-step Solution

1

Rewrite $\frac{{\left(-1\right)}^n\left(x-2\right)^n}{3^n\sqrt{n^2+1}}$ using the property of the power of a quotient: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

$\frac{{\left(\left(-\frac{1}{3}\right)\right)}^n\left(x-2\right)^n}{\sqrt{n^2+1}}$

Final answer to the exercise

$\frac{{\left(\left(-\frac{1}{3}\right)\right)}^n\left(x-2\right)^n}{\sqrt{n^2+1}}$

Try other ways to solve this exercise

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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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