Which of the following statements is correct?

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(D) Let us analyze each option:$1$. For $\sqrt{x^2} = |x|$,by definition of the principal square root,$\sqrt{x^2}$ is always non-negative and equals t

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(D) Let us analyze each option:$1$. For $\sqrt{x^2} = |x|$,by definition of the principal square root,$\sqrt{x^2}$ is always non-negative and equals the absolute value of $x$. This is correct.$2$. For $x^{x+1} = x \cdot x^x$,using the laws of exponents,$x^1 \cdot x^x = x^{1+x} = x^{x+1}$. This is correct.$3$. For $\frac{|x|}{x}$,if $x > 0$,then $|x| = x$,so $\frac{x}{x} = 1$. If $x Since all statements are correct,the answer is $D$.

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