Simplify ( square root of x^2+1)^2

${(\sqrt{x^{2} + 1})}^{2}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2} + 1}$ as ${(x^{2} + 1)}^{\frac{1}{2}}$ .

${({(x^{2} + 1)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{2} + 1)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

${(x^{2} + 1)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x^{2} + 1)}^{\frac{2}{2}}$

Rewrite the expression.

${(x^{2} + 1)}^{1}$

Simplify.

$x^{2} + 1$