Simplify ((32x^10)/(2x^8))^(1/2)

${(\frac{32 x^{10}}{2 x^{8}})}^{\frac{1}{2}}$

Cancel the common factor of $32$ and $2$ .

Factor $2$ out of $32 x^{10}$ .

${(\frac{2 (16 x^{10})}{2 x^{8}})}^{\frac{1}{2}}$

Cancel the common factors.

Factor $2$ out of $2 x^{8}$ .

${(\frac{2 (16 x^{10})}{2 (x^{8})})}^{\frac{1}{2}}$

Cancel the common factor.

${(\frac{2 (16 x^{10})}{2 x^{8}})}^{\frac{1}{2}}$

Rewrite the expression.

${(\frac{16 x^{10}}{x^{8}})}^{\frac{1}{2}}$

Cancel the common factor of $x^{10}$ and $x^{8}$ .

Factor $x^{8}$ out of $16 x^{10}$ .

${(\frac{x^{8} (16 x^{2})}{x^{8}})}^{\frac{1}{2}}$

Cancel the common factors.

Multiply by $1$ .

${(\frac{x^{8} (16 x^{2})}{x^{8} \cdot 1})}^{\frac{1}{2}}$

Cancel the common factor.

${(\frac{x^{8} (16 x^{2})}{x^{8} \cdot 1})}^{\frac{1}{2}}$

Rewrite the expression.

${(\frac{16 x^{2}}{1})}^{\frac{1}{2}}$

Divide $16 x^{2}$ by $1$ .

${(16 x^{2})}^{\frac{1}{2}}$

Simplify the expression.

Apply the product rule to $16 x^{2}$ .

$16^{\frac{1}{2}} {(x^{2})}^{\frac{1}{2}}$

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

Evaluate the exponent.

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

Multiply the exponents in ${(x^{2})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$4 x^{1}$

Simplify.

$4 x$

Simplify ((32x^10)/(2x^8))^(1/2)

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