Simplify cube root of (x-5)^6

$\sqrt[3]{{(x - 5)}^{6}}$

Rewrite ${(x - 5)}^{6}$ as ${({(x - 5)}^{2})}^{3}$ .

$\sqrt[3]{{({(x - 5)}^{2})}^{3}}$

Pull terms out from under the radical, assuming real numbers.

${(x - 5)}^{2}$

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$(x - 5) (x - 5)$

Expand $(x - 5) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$x (x - 5) - 5 (x - 5)$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 (x - 5)$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5$

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x - 5 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$x^{2} - 5 x - 5 x + 25$

Subtract $5 x$ from $- 5 x$ .

$x^{2} - 10 x + 25$