Simplify ((4m-2n^8)/(9m-6n-8))^(1/2)

${(\frac{4 m - 2 n^{8}}{9 m - 6 n - 8})}^{\frac{1}{2}}$

Step 1

Factor $2$ out of $4 m - 2 n^{8}$ .

Factor $2$ out of $4 m$ .

${(\frac{2 (2 m) - 2 n^{8}}{9 m - 6 n - 8})}^{\frac{1}{2}}$

Factor $2$ out of $- 2 n^{8}$ .

${(\frac{2 (2 m) + 2 (- n^{8})}{9 m - 6 n - 8})}^{\frac{1}{2}}$

Factor $2$ out of $2 (2 m) + 2 (- n^{8})$ .

${(\frac{2 (2 m - n^{8})}{9 m - 6 n - 8})}^{\frac{1}{2}}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 (2 m - n^{8})}{9 m - 6 n - 8}$ .

$\frac{{(2 (2 m - n^{8}))}^{\frac{1}{2}}}{{(9 m - 6 n - 8)}^{\frac{1}{2}}}$

Apply the product rule to $2 (2 m - n^{8})$ .

$\frac{2^{\frac{1}{2}} {(2 m - n^{8})}^{\frac{1}{2}}}{{(9 m - 6 n - 8)}^{\frac{1}{2}}}$