Simplify (- square root of x-4)^2

${(- \sqrt{x - 4})}^{2}$

Simplify the expression.

Apply the product rule to $- \sqrt{x - 4}$ .

${(- 1)}^{2} {\sqrt{x - 4}}^{2}$

Raise $- 1$ to the power of $2$ .

$1 {\sqrt{x - 4}}^{2}$

Multiply ${\sqrt{x - 4}}^{2}$ by $1$ .

${\sqrt{x - 4}}^{2}$

Rewrite ${\sqrt{x - 4}}^{2}$ as $x - 4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 4}$ as ${(x - 4)}^{\frac{1}{2}}$ .

${({(x - 4)}^{\frac{1}{2}})}^{2}$

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

${(x - 4)}^{\frac{1}{2} \cdot 2}$

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

${(x - 4)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x - 4)}^{\frac{2}{2}}$

Rewrite the expression.

${(x - 4)}^{1}$

Simplify.

$x - 4$