Write as a Set of Linear Factors (x-5)^(2/3)=16

${(x - 5)}^{\frac{2}{3}} = 16$

Subtract $16$ from both sides of the equation.

${(x - 5)}^{\frac{2}{3}} - 16 = 0$

Rewrite ${(x - 5)}^{\frac{2}{3}}$ as ${({(x - 5)}^{\frac{1}{3}})}^{2}$ .

${({(x - 5)}^{\frac{1}{3}})}^{2} - 16 = 0$

Rewrite $16$ as $4^{2}$ .

${({(x - 5)}^{\frac{1}{3}})}^{2} - 4^{2} = 0$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = {(x - 5)}^{\frac{1}{3}}$ and $b = 4$ .

$({(x - 5)}^{\frac{1}{3}} + 4) ({(x - 5)}^{\frac{1}{3}} - 4) = 0$

Write as a Set of Linear Factors (x-5)^(2/3)=16

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